Question

The sides of an isosceles triangle are 14.0m, 14.0m, and 18.0m. Find the size of each angle of the triangle.

Answer 1

Draw the isosceles triangle:

In a isosceles triangle two sides and two angles are equal.

Find the angle x by using the sine rule:

14/sin x  = 18 / sin (180 − 2x)

Apply trigonometric angle formula: sin (180 − x) = sin x

14/sin x  = 18 / sin (2x)

Apply trigonometric double angle identities: sin (2x) = 2sin x cos x

14/sin x  = 18 / 2 sin x cos x

18 sin x  = 28  sin x cos x

9 sin x  = 14  sin x cos x

9 sin x  - 14  sin x cos x = 0

sin x ( 9  - 14 cos x ) = 0

sin x = 0

x = π is not possible.

9  - 14 cos x = 0

cos x  = 9/14

x  = 50 degree

180 - 2x = 80 degree

Therefore, the angles are 50,50, and 80.