Two electricity pylons P and Q are 550m apart on the same side of a river. A third pylon R is on the other side of the river. Angle RQP is 62° and Angle QRP is 70°. Find by calculation the distance from R to Q to the nearest metre
Two electricity pylons P and Q are 550m apart on the same side of a river. A third pylon R is on the other side of the river. Angle RQP is 62° and Angle QRP is 70°. Find by calculation the distance from R to Q to the nearest metre
Angle Q is 62° and angle R is 70°, so angle P is 48°.
Use the Law of Sines:
$\displaystyle \frac{\sin P}{p} = \frac{\sin R}{r}$
(p is side QR and r is side PQ)
Plug the numbers in:
$\displaystyle \frac{\sin 48^{\circ}}{p} = \frac{\sin 70^{\circ}}{550}$
and solve for p.
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