Question

50 POINTS EACH

Answer 1

Since s and t are complimentary, that means ∠s + ∠t = 90

From the picture, we also know that ∠t + ∠LGM = 90

Set them equal to each other:

∠s + ∠t = ∠t + ∠LGM, solve:

∠s = ∠LGM

Now using the fact that tangent = opposite/adjacent:

tan (∠s) = $\frac{y}{h}$

tan (∠s) = $\frac{h}{x}$

Set them equal to each other to get:

$\frac{y}{h}$ = $\frac{h}{x}$

Solve:

$h^{2}= xy\\h = \sqrt{xy}$

Part B:

Using tan (∠s) = $\frac{y}{h}$

We get: $h = \frac{3}{tan38} = 3.84$ meters

Hope that helps!