Question

To determine the distance across a pond, Harrymade the measurements shown in the diagram.ROS20 m80°TWhich is closest to the distance from R to S?3.48 m19.7 m20.3 m113.4 m

Answer 1

From the drawing made, we can see that a triangle with a right angle is form, thus, a right triangle.

Since this is a right triangle, the properties of sine, cossine and tangent apply. RS is the leg opposite to the 80° angle, while 20m is the length of the hypotenuse. So we can use sine to find RS.

$\begin{gathered} \sin 80\degree=\frac{RS}{ST}=\frac{RS}{20} \\ RS=20\sin 80\degree\approx20\cdot0.9848=19.696\approx19.7 \end{gathered}$

So, the closest alternative is 19.7 m.