Question

Find x
Use trigonometry

Answer 1

x ≈ 17.9°

Explanation:

Calculate the length of the common segment ( line shared by both triangles )

let this segment be y.

using the tangent ratio in the lower right triangle

tan37° =
`(opposite)/(adjacent)` =
`(y)/(3)` ( multiply both sides by 3 )

3 × tan37° = y , then

y ≈ 2.26 ( to 2 decimal places )

using the tangent ratio in the upper right triangle

tan x =
`(opposite)/(adjacent)` =
`(y)/(7)` =
`(2.26)/(7)` , then

x =
`tan^(-1)` (
`(2.26)/(7)` ) ≈ 17.9° ( to 1 decimal place )