



 
Hi Becc, You can draw the triangle if you wish. Draw a line segment of length 3.1 cm and label the endpoints a and b. Set the point of a compass at a and with a radius of 4 cm draw an arc of a circle. Move the compass point to b and draw an arc of radius 2 cm draw another arc. Call the intersection of the arcs c. Complete the triangle abc. You can now measure the height. The value you obtain for h depends on the accuracy with which you can measure, both the measurement of h and the measurements in the construction. A better way to find the height is to use algebra. Draw a triangle and label it abc. Draw a line from c, perpendicular to ab to meet ab at d. CD = is the height of the triangle. Let ad = x. (In the construction I found that the triangle is obtuse but that's not how I drew the triangle above. The calculations will show that abc is obtuse.) Triangles adc and dbc are right triangles so using Pythagoras theorem
and
Substituting your numbers
and
Solve these equations for x and then substitute the value for x into 4^{2} = h^{2} + x^{2} to find h. When you do this you will see that x is larger than ab = 3.1 cm so d is to the right of b and the triangle is obtuse. Penny  


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