Question

Jasmine is going on a trip with her friend George. Theyboth decide to meetup at the location of the resort. Thedestination is at a 66 degree angle from Jasmine'shouse and a 53 degree angle from George's house. Ifthere is a 20 mile distance between George andJasmine respective houses, how far does George haveto drive to arrive at the resort? How far does Jasminehave to drive? For a visual aid see the attachment.*Triangle not drawn to scale.*

Answer 1

The total angles in a triangle are 180degrees.

Therefore,

$\begin{gathered} a+66^0+53^0=180^0 \\ a=180^0-(66^0+53^0)=61^0 \\ \therefore a=61^0 \end{gathered}$

In order to solve for the distances of the other two sides, we will use the Sine rule formula.

which says,

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

Where,

$\begin{gathered} \text{Jasmine's distance=b} \\ \text{George's distance=c} \\ R\text{esort}=a=20\text{miles} \\ A=61^0,B=66^0,C=53^0 \end{gathered}$

Solving for George's distance (c)

$\begin{gathered} \frac{\sin61^0}{20}=\frac{\sin53^0}{b} \\ c=\frac{s\text{in}53^0\times20}{\sin61^0}=\frac{0.79863551\times20}{0.8746197071}=18.26246318\approx18.26(nearest\text{ hundredths)} \\ c=18.26\text{miles} \end{gathered}$

Solving for Jasmine distance (b)

$\begin{gathered} \frac{\sin A}{a}=\frac{\sin B}{b} \\ \frac{\sin61^0}{20}=\frac{\sin66^0}{c} \\ b=\frac{\sin66^0\times20}{\sin61^0}=\frac{0.9135454576\times20}{0.8746197071}=20.8901183\approx20.89(nearest\text{ hundredths)} \\ \therefore b=20.89miles \end{gathered}$

Hence,

Jasmine will drive 20.89miles to arrive at the resort.

George will drive 18.26miles to arrive at the resort.