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.

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