Question

What are the values of w and x in the triangle below? Round the answers to the nearest tenth.thank you ! :)

Answer 1

w = 14.4

x = 11.2

Step-by-step explanation:

We would consider the smaller and larger right angle triangles.

For the smaller right triangle, taking 48 as the reference angle,

opposite side = 16

adjacent side = w

We would find w by applying the tangent trigonometric ratio which is expressed as

tanθ = opposite side/adjacent side

Thus,

tan48 = 16/w

By cross multiplying,

wtan48 = 16

w = 16/tan48

w = 14.4

For the larger right triangle, taking 32 as the reference angle,

opposite side = 16

adjacent side = w + x = 14.4 + x

We would find w by applying the tangent trigonometric ratio which is expressed as

tanθ = opposite side/adjacent side

Thus,

tan32 = 16/(14.4 + x)

By cross multiplying,

(14.4 + x)tan32 = 16

(14.4 + x) = 16/tan32

14.4 + x = 25.6

x = 25.6 - 14.4

x = 11.2