Expert: Paul Klarreich - 1/27/2007

Question
The vertex angle of an isosceles triangle is 57 degrees 24' and each of its equal sides is 375.5 ft long. Find the altitude of the triangle.

Answer
Questioner:   Tracey
Category:  Advanced Math
Private:  no
 
Subject:  Plane Trig
Question:  The vertex angle of an isosceles triangle is 57 degrees 24' and each of its equal sides is 375.5 ft long. Find the altitude of the triangle.
.......................................................
Hi, Tracey,

In your triangle ABC, with AB=AC, you will first DRAW the altitude AD.  Then you will be able to prove that it bisects the vertex angle, and so angle BAD = half of 57 24' = 28 42'.

Now triangle ADB is a right triangle, and in it,

Angle BAD is 28 42'
AB = 375.5 is the hypotenuse.
AD is the leg adjacent to angle BAD, so you will use the cosine.
             AD
cos 28 42' = -----
            375.5

AD = 375.5 cos 28 42'

You may have to do some arithmetic to make your calculator handle 28 42' as a number of degrees and decimal parts, but that's it.