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 6 miles along a bearing of N32°W which brings her to the Muffin Ridge Observatory. From there, she knows a bearing of S42°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?

NOTE: Here is the meaning of the bearings notation used in this problem:
1) N32°W means: Relative to (or starting with) the North direction, go 32° West
2P S42°E means: Relative to (or starting with) the South direction, go 42° East

Answer 1

Solution-

Let the three positions Sasquatch Point, Chup acabar Trailhead and Muffin Ridge are denoted by A, B and C respectively.

Now according to question, a hiker starts walking due west from Sasquatch Point (A) and gets to the Chupacabra Trailhead (B). From the Chupacabra Trailhead (B) she hikes for 6 miles along a bearing of N32°W which brings her to the Muffin Ridge Observatory (C). From there(C), she knows a bearing of S42°E will take her straight back to Sasquatch Point(C).

Let ll' and mm' represents the North-South directions at point B and C respectively.

This situation is shown in the figure below-

M ccmuffin Ridge obsegundssy) ar 27 .W 6 mill B cerupacabana l Trailhead "A (Sasquatch Point)

Now,

Angle B = 90° + 32° =112°

Since <BCm' = <CBl = 32°

So,

Angle C = 42° - 32° = 10°

And

<A =180° -(<B + <C) = 180° -(112° + 10°) = 58°

Let the opposite sides of angles A, B and C of the triangle formed are a , b and c respectively.

So, a = 6 miles and b is the distance to be find out.

As shown in figure below-

(muffin Ridge observatory) ( 10° b 6miles a 1120 580 A (sqsquat Ich Point) B (Chapa cabra Trailhead')

We know that the sine formula is

$\frac{a}{sin(A)}=\frac{b}{sin(B)}=\frac{c}{sin(C)}$

On putting the values , a = 6 miles, A = 58°, B = 112° , C = 10°, we get

$\frac{6}{sin(58^o)}=\frac{b}{sin(112^o)}=\frac{c}{sin(10^o)}$

This implies

$\frac{6}{sin(58^o)}=\frac{b}{sin(112^o)}$

Or

$sin(112^o)\frac{6}{sin(58^o)}=b$

$b=sin(112^o)\frac{6}{sin(58^o)}$

$b=(0.92718)\frac{6}{(0.848048)}$

Hence, she have to walk 6.6 miles to get from the Muffin Ridge Observatory to Sasquach Point.