Question

What is the distance between the hiker and the bear?

Answer 1

Let's make a diagram to represent the question

The angles of depression so made has angles of elevation as seen below that are corresponding.

This has made a two right-triangles with 10 degrees and 15 degrees respectively.

To find the distance between the Hiker and the angry Bear, we need to find the distance between the fire tower and the Angry Bear, labelled as D

Then the distance between the Hiker and the fire tower labeled as x, Then

Subtract D from x to get our answer, which is d.

Side D becomes, from trig SOHCAHTOA

`\begin{gathered} TOAtan\theta=(opposite)/(adjacent) \\ tan10\degree=(157)/(D) \\ tan10\degree D=157 \\ D=(157)/(tan10\degree) \\ D=890.3912\text{ feet} \end{gathered}`

Side x becomes

`\begin{gathered} tan\theta=(opposite)/(adjacent) \\ tan15\degree=(157)/(x) \\ tan15\degree=(157)/(x) \\ tan15\degree x=157 \\ x=(157)/(tan15\degree) \\ x=585.9320\text{ feet} \end{gathered}`

Side d becomes

`\begin{gathered} d=D-x \\ d=890.3912-585.9320 \\ d=304.4592 \end{gathered}`

hence the answer is 304 feet to the nearest foot