Question

A hiker starts walking due west from Sasquatch Point and gets to the Chupacabra Trailhead before she realizes that she hasn't reset her pedometer. From the Chupacabra Trailhead she hikes for 8 miles along a bearing of N27°W which brings her to the Muffin Ridge Observatory. From there, she knows a bearing of S38°E will take her straight back to Sasquatch Point. How far will she have to walk to get from the Muffin Ridge Observatory to Sasquach Point, to the nearest tenth of a mile?

Answer 1

9.05 mile

Explanation:

From the information given :

Let represent S for Sasquatch Point

Let C represent Chupacabra Trailhead

Let M represent Muffin Ridge Observatory

The diagram for the bearing of the information given can be seen in the attached file below.

At angel C = 90° -27° = 63°

The Alternate angles are shown in the second diagram below.

In order to determine the distance she will have to walk from the Muffin Ridge Observatory to Sasquatch Point, we use the sine formula:

`\mathtt{(sin \ C )/(c) = (sin \ S)/(s)}`

`\mathtt{(sin \ 63 )/(c) = (sin \ 52)/(8)}`

By cross multiply

8 × sIn 63 = c× sin 52

`\mathtt{c = (8 * Sin 63)/(Sin \ 52)}`

`\mathtt{c = (7.1281)/(0.7880)}`

c = 9.0458 mile

c
`\simeq` 9.05 mile to the nearest tenth