Tower on a slope problem

Question

I have the following setup:

Nothing else is known apart from the 2 distances and the 2 angles and I need to calculate h. How can I do this?

Answer 1

In the triangle with side lengths: $h$ and $30$, you can find the length of the other side. Call this length, $x$. Then by the Sine Rule,

$$\frac{x}{\sin 22.92}=\frac{50}{\sin (180-22.92-(180-44.47))}$$

Then use the Law of Cosines to find $h$:

$$h^2=x^2+30^2-60x\cos 44.47$$

Answer 2

HINT

Use the law of sines for triangles $$\frac{\sin \alpha}{a}=\frac{\sin \beta}{b}=\frac{\sin \gamma}{c}$$