Question

Each base of an isosceles triangle measures 42 degrees, 30'. The base is 14.6 meters long.
a. Find the length of a leg of the triangle
b. Find the altitude of the triangle
c. What is the area of the triangle?

Answer 1

make a sketch, marking the angles

draw the altitude, cutting the base into 2 parts of 7.3 each, and giving you right-angled triangles.

a) leg of triangle = hypotenuse of the right-angled triangle, call it c
cos 42.5 = 7.3/c
c = 7.3/cos 42.5 = ....
b) altitude --- h
tan 42.5 = h/7.3
h = 7.3tan 42.5 = ....

c) area - (1/2) base x heigh
= (1/2)(14.6)(h) , the h from b)
= ....