Question

A straight driveway is 76 ft long and the top is 10 ft above the bottom what angle does it make with the horizontal?

Answer 1

You can model this situation with a right triangle ABC, where AB is the horizontal leg, and BC is the vertical leg:

$\quad\quad\quad\quad\quad C\\\\A\quad\quad\quad\quad\; B$

We know that BC=10 and AC=76.

We are interested in angle A.

Using the law of sines, we know that

$\dfrac{BC}{\sin(A)}=\dfrac{AC}{\sin(90)}\iff \dfrac{BC}{\sin(A)}=AC \iff \sin(A)=\dfrac{BC}{AC}=\dfrac{10}{76}$

So, the angle is

$\sin(A)=\dfrac{10}{76}\implies A=\arcsin\left(\dfrac{10}{76}\right)$