Question

A person starts out 17 miles from the base of a tall mountain, and looks up at a 4 angle of elevation to the top of the mountain. When they move 12 miles closer to the base of the mountain, what will be their angle of elevation when they look to the top? Answer to the nearest degree.

Answer 1

$\sf{Trigonometric\:ratios}$:

$\boxed{\sf{Tan\:(4)\:degrees = \frac{Opposite}{17}}}$

$\sf{\underline{Opposite}}$:

$\implies$ tan (4) x 17

$\implies$ 1.2

$\sf{\underline{We\:know\:that}}$:

$\bullet$ He moves 12 miles closer.

$\bullet$So 5 miles from mountain.

$\sf{\underline{Using}}$:

$\implies$ $\sf{tan = \frac{Opposite}{Adjacent}}$

$\implies$ $\sf{tan = \frac{1.2}{5}}$

$\implies$ $\sf{tan = 0.24}$

$\sf{\underline{That\:is}}$:

$\boxed{\sf{tan^{-1} = 13.5\degree}}$

$\sf{\underline{Therefore}}$:

When they move 12 miles closer to the base of the mountain, their angle of elevation will be 13.5°