Side lengths and area of a triangle

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Question from angela, a student:

in the diagram of ABC the angle A is 65 the angle B is 70 and the side opposite vertex B is 7. Find the length of the side opposite vertex A and find the area of ABC

Thanks for your help

Hi Angela,

Since the sum of the measures of the angles in a triangle is 180 degrees the measure of the angle at C is 180 - (65 + 70) degrees. Now you can use the Law of Sines to find the lengths of the remaining two sides.

You can calculate the area in two different ways. If you want to use the formula that the area of a triangle is half the base times the height you need to decide which side to call the base and then calculate the height. One choice is to take the side BC to be the height and then convince yourself that the height is 7 × sin(C).

I hope this helps,
Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.