







Angles of elevation and depression 
20150308 

From Timmy: Joel is walking down a street and sees a 115 ft tall building in front of him. He stops 190 feet from the base of the building at the tip of the building's shadow. Round answers to three decimal places.
A. If there was a piece of rope from the top of the building to Joel, how long would it be?
B. What is the angle of elevation from Joel to the top of the building?
C. Margaret says that she could find the angle of depression from the top of the building to Joel by subtracting the angle of elevation from 90°. Is she correct? Explain. Answered by Penny Nom. 





The height of a building 
20150120 

From Emily: A man 2m high observes the angle of elevation to the top of the building to be 70 degrees. And the angle of depression to the bottom of the building to be 19 degrees. How tall is the building? Answered by Robert Dawson. 





A ladder against a wall 
20140709 

From thabo: A ladder 6.5m long,leans against a wall so that the top of the ladder is 4.8m from the ground.what is the angle of elevation of the ladder to the top of the wall Answered by Penny Nom. 





The angle of elevation of the sun 
20130703 

From Maurice: A vertical pole with a length of 7m cast a shadow with a length of 5m. Calculate the angle of elevation of the sun and include a diagram. Answered by Penny Nom. 





The angles of elevation and depression 
20121203 

From Chelsey: a person on a balcony of one building looks towards a second building. if the angle of elevation to the top of the second building is 25 degrees, the angle of depression to the bottom of the second building is 17 degrees, and the balcony of the first building is 22 feet above the ground, what is the height of the second building? Answered by Penny Nom. 





The height of a building 
20120908 

From Lin: How do surveyors determine a height of a building 150 feet away with an observation angle at 40 degrees?
What is the elevation of that top floor? Answered by Penny Nom. 





The angular elevation of the sun 
20120714 

From VINEET: WHAT IS ANGULAR ELEVATION OF THE SUM Answered by Penny Nom. 





What is the height of the building? 
20110205 

From Myra: The angle of elevation is 45 degrees. The distance from George's foot to the top of the building is 50m. What is the height of the building? Answered by Penny Nom. 





Angle of elevation 
20101210 

From PANKAJ: angle of elevation of the sun perpendicular72 and base 88 find angle Answered by Penny Nom. 





A building and a flag pole 
20100909 

From paul: A flag pole and a building stand on the same horizontal level. From the point p at the bottom of the building,the angle of elevation of the top t of the flag pole is 65 degrees. From the top q of the building the angle of elevation of the point t is 25 degrees.If the building is20 meters high. Calculate the distance pt Answered by Penny Nom. 





80,000 yards of dirt 
20100812 

From Jeremy: If I have an area 50' x 1200', what would be the elevation with 80,000 yards of dirt on it. Answered by Robert Dawson. 





The height of a flag shaft 
20100425 

From Sarah: A man standing 20metres away from a tower observes the angles of elevation to the top and bottom of a flag shaft standing on the tower as 62degrees and 60degrees respectively. Calculate the height of the flag shaft.' Answered by Penny Nom. 





How far apart are the two girls? 
20100118 

From benny: Debby and john are looking up at their house from the backyard. From Debby's
point of view, the top of the house is at an angle of elevation of 40 degrees
From Johns point of view, directly closer to the house, it is 60 degrees. The
house is 15m high. How far apart are the two girls? Answered by Robert Dawson. 





A vertical radio tower is located on the top of a hill 
20090421 

From Rafael: A vertical radio tower is located on the top of a hill that has an angle of elevation of 10 degrees. A 70foot guy wire is attached to the tower 45 feet above the hill.
a. Make a drawing to illustrate the situation
b. What angle does the guy wire make with the side of the hill?
c. How far from the base of the tower is the guy wire anchored to the hill?
What confuses me about this problem is the visual situation. Isn't the angle of the guy wire with the side of the hill the same as the angle of elevation? And if not, then how is one supposed to find the other angles without any more information? Answered by Harley Weston. 





Confusion in a multiple choice question 
20081114 

From BJ: My son got this math problem which he could mostly solve. Here it is:
The highest location in a certain country is 4525 m above sea level. The lowest point in the same country is 192 m below sea level.
a) Find the difference of the two elevations. His answer: a(b)= a+b or 4525(192)= 4525+192=4717 m. No problem.
b) A city is 2221 m above sea level. Is this elevation closer to the highest point or the lowest point?
His answer: highest point because: 45252221= 2304 m (closest to the highest point) and 2221(192)=2221+192= 2413 m. (farthest to the lowest point). OK so far.
But then he was given 4 choices for this question with no other information:
a) 4717 m; lowest b) 4333 m; lowest c) 4333 m; highest d) 4717 m; highest
What does it mean? What's the connection with the rest of the problem? Answered by Harley Weston. 





How tall is the wall? 
20080929 

From ash: you and bob are separated by a tall wall you stand 10 feet further from the wall
than bob your angle of elevation is 37 degrees and his 44 degrees
how tall is the wall? Answered by Penny Nom. 





Angle of elevation 
20080909 

From kristy: A man on the tenth floor of a building shouts down to a person on the street. If the angle of elevation from the street to the man in the building is 35° and the man in the building is 40 feet up, about how far away from the building is the person on the street? Answered by Penny Nom. 





The height of a tree 
20080909 

From danice: At a certain time of day, the angle of elevation of the sun is 30°. A tree has a shadow that is 25 feet long. Find the height of the tree to the nearest foot. Answered by Penny Nom. 





Angle of Elevation 
20080129 

From Rita: Uluru or Ayers Rock is a sacred place for Aborigines of the western desert of Australia.
ChunWei uses a surveying device to measure the angle of elevation to the top of the rock to be 11.5 degrees.
He walks half a mile closer and measures the angle of elevation to be 23.9 degrees.
How high is Ayers Rock in feet? Answered by Stephen La Rocque. 





The elevation of the sun 
20070910 

From Elena: The "angle of elevation" of an object about you is the angle between a horizontal line of sight between you and the object. (See figure) After the sun rises, its angle of elevation increases rapidly at first, then more slowly, reaching a maximum near noontime. Then the angle decreases until sunset. The next day the phenomenon repeats itself. Assume that when the sun is up, its angle of elevation (E) varies sinusoidally with the time of day. Let t be the number of hours that has elapsed since midnight last night. Assume that the amplitude of this sinsoid is 60 degrees, and the maximum angle of elevation occurs at 12:45 p.m.. Assume that at this time of year the sinusoidal axis is at E=5 degrees. The period is, of course, 24 hours.
a. Sketch a graph of this function
b. What is the realworld significance of the t  intercepts?
c. What is the real world significance of the portion of the sinusoid, which is below the taxis?
d. Predict the angle of elevation at 9:27 a.m., and at 2:30 p.m.
e. Predict the time of sunrise
f. As you know, the maximum angle of elevation increases and decreases with the change of the seasons. Also, the times of sunrise and sunset change with the seasons. What one change could you make to your mathematical model that would allow you to use it for predicting the angle of elevation of the sun at time on any day of the year. Answered by Harley Weston. 





The height of a pole 
20070802 

From lalaine: Hi, this is my problem..
From a point 50.2 m to the pole, a student measured the angle of elevation to the top of the pole to be 32°. Find the height of the pole if the student's height from his feet to his eyes is about 4 ft. Answered by Penny Nom. 





Angle of inclination from the horizontal 
20070718 

From Joyce: In flying upward for 1260 yards along a straight inclined path airplane rises
156 yards. Find the climbing angle
( the angle of inclination from the horizontal)
Thank you in advance Answered by Stephen La Rocque. 





Height of a tower from two observations 
20070716 

From joyce: An observer wishes to determine the height of a tower. He takes sight @
the top of the tower from A & B w/c are 5oft. apart @
the elevation on a direct line w/ the tower.
The vertical angle @ point A is 30 degrees & the point B is 40 degrees.
What is the height of the tower?
Find the value of x in angle tangent 40 degrees and 30 degrees?
Show the solution of the value of x? Answered by Stephen La Rocque. 





Height of an antenna (angle of elevation) 
20070716 

From Fhay: An antenna stands on the edge of the top of a 52 story building from a point 320 ft. from the base of the building, the angle of elevation to the top of the antenna is 64 degrees in each story is 12 ft. high. Find the height of the antenna Answered by Stephen La Rocque. 





The two towers (angles of elevation trigonometry) 
20070714 

From joyce: The angle of elevation of tower B from the top of tower A is 28 degrees
and the angle of elevation of the top of tower A from the base is 46 degrees
Find the height of tower A if tower B is 120 m high? Answered by Stephen La Rocque. 





Angles of depression 
20070613 

From Phonda: The pilot of a small private plane can look forward and see the control tower for a small airstrip. Beyond that is a large factory that is 3 milies from the airstrip. The angles of depression are 12.5 degrees and 4.8 degrees respectively.
Find the airplane's altitude, to the nearest ten feet. Answered by Stephen La Rocque. 





Angle of elevation 
20070313 

From Joslyn: A ship at sea sights a 12m high lighthouse on a cliff which is 80m above sea level.
If the angle of elevation to the top of the lighthouse is 27 degrees, calculate the distance from the ship to the shore. Answered by Haley Ess. 





Angle of elevation 
20070205 

From Zee: A 55 ft. flagpole casts a 25 ft. shadow. Calculate the angle of elevation to the sun to the nearest degree. Answered by Stephen La Rocque. 





Percent elevation gain 
20070124 

From Susan: okay... so if I hike Gregory Canyon and it's a 1.1 mile hike with a 900 foot elevation gain, what's the percent elevation gain? Answered by Stephen La Rocque. 





The waterway between Lake Huron and Lake Superior 
20060321 

From Trenae: the waterway between lake huron and lake superior separates the u.s and canada.it is usually 13 feet above the water when its closed and each section is 210 feet long if the angle of elevation is 70 degrees then what is the distance from the top of the drawbridge to the water and the width of the gap created by the 2 sections of the bridge Answered by Penny Nom. 





Two word problems 
20051114 

From Jennifer:
1. Every other person on a school's parent advisory committee is surveyed to determine how many people support passage of a school bond to build a new elementary school. Is this a good sample? Why or why not?
2.What is the difference in elevation between the highest point in California,Mount Whitney,which towers 4421 meters above sea level, the lowest point in California,Death Valley, which lies 86 meters below sea level?
Answered by Harley Weston. 





The elevation of the top of the house 
20051113 

From Chloe: Karen is standing 23 metres away from the base of a 23 metre high house. Assume that Karen's eyes are 1.5 metres above ground. Find the elevation of the top of the house from Karen's eye line. Answered by Penny Nom. 





Angles of elevation and depression 
20040518 

From Anjum: what is the difference between an angle of elevation and angle of depression? Answered by Penny Nom. 





The angle of elevation 
20010308 

From Jeffrey: At a Certain time, a vertical pole 3m tall cast a 4m shadow. What is the angle of elevation of the sun? Answered by Harley Weston. 

