# GEOM 2 | Lesson 2 | Practice 3 Solutions

1.  Horizontal distance $$(x)$$ :

$$\tan 15˚ =\dfrac{10,000}{x}$$

$$x = \dfrac{10,000}{\tan 15˚}$$  so $$x = 37,320.5$$ ft.

Distance the plane needs to travel (hypotenuse, $$h$$) :

$$\sin 15^\circ = \dfrac{10,000}{h}$$

$$h = \dfrac{10,000}{\sin 15^\circ}$$

$$h = 38,637.03$$

2.

$$\tan 12˚ = \dfrac{12,000}{x}$$

$$x = \dfrac{ 12,000}{\tan 12˚}$$ or $$x = 56,455.6$$ ft

Using the pythagorean theorem, find $$y$$:  $$y = 57,716.8$$ ft

3.

$$\tan 35˚ = \dfrac{x}{25}$$

$$x = 25 \tan 35˚$$ ; $$x = 17.5$$ ft

But 5.5 needs to be added to it as the angle of elevation was taken from eye height.

The tree is $$23$$ft.