Question

Solve for the Unknow with full explanation

Answer 1

θ ≈ 31.9°

Explanation:

begin by finding the value of x

using Pythagoras' identity in the right triangle

(x + 8)² = x² + 28² ← expand left side using FOIL

x² + 16x + 64 = x² + 784 ( subtract x² from both sides )

16x + 64 = 784 ( subtract 64 from both sides )

16x = 720 ( divide both sides by 16 )

x = 45

using the tangent ratio in the right triangle

tanθ =
`(opposite)/(adjacent)` =
`(AB)/(AC)` =
`(28)/(x)` =
`(28)/(45)` , then

θ =
`tan^(-1)` (
`(28)/(45)` ) ≈ 31.9° ( to 3 significant figures )