Question

A hiker is hiking up a 12-degree slope. If she hikes 15 miles, how much attitude (vertical height) doesshe gain?

Answer 1

we can make a triangle

we need to find x

we can use the trigonometric ratio of sine

`\begin{gathered} \sin (\alpha)=(O)/(H) \\ \end{gathered}`

where alpha is the angle, O the opposite side from the angle and H the hypotenuse

so placing

`\begin{gathered} \sin (12)=(x)/(15) \\ \\ x=15\sin (12) \\ x=3.12 \end{gathered}`

she climbs 3.12 miles vertically