Patricia and Trent are 48 m apart. The angle of elevation from Patricia to the hot air balloon hovering in the sky between her and the Trent is 43 degrees, while the angle of elevation from Trent to the balloon is 31 degrees.
a.) Draw a diagram of the situation
b.) Determine the distance between the ballon and the person farthest from the balloon. Round to th nearest tenth of a metre.
6 years ago
Answered By Eric C
This question is an excellent example of the sine law:
$\left(\frac{a}{\sin A}\right)=\left(\frac{b}{\sin B}\right)=\left(\frac{c}{\sin C}\right)$(asinA )=(bsinB )=(csinC )
What we need is the ratio of the length of a leg to the sine of the angle opposite to it.
The length of the distance between Patricia and Trent is 48 m. The angle opposite is determined by:
$B=180-43-31=106^{\circ}$B=180−43−31=106?
The ratio therefore is:
$\frac{48}{\sin106}=49.9$48sin106 =49.9
knowing that:
$\frac{a}{\sin A}=\frac{b}{\sin B}=49.9$asinA =bsinB =49.9
Multiply both sides by the sine of angle A gives the distance a:
$a=49.9\times\sin43=34.1m$a=49.9×sin43=34.1m
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