Question

An isosceles triangle has an area of 254 km², and the angle between the two equal sides is 53°. Find the length of the two equal sides

length of equal sides

Answer 1

Area of a triangle = 1/2 ab sinC

In this equation the angle C is between the two adjacent sides ab
Since the lengths are equal we can call them both X
Hence 254= 1/2 (x)(x) sin53
By simplifying 508 = (x^2) sin53
So therefore x is the square root of 508 divided by sin53 which means the length of the sides is 35.8km to 3 significant figures