Question

Two points A and B are on opposite sides of a building. A surveyor chooses a thirdpoint C 73 yd from B and 101 yd from A, with angle C measuring 53.5°. How far apartare A and B (to the nearest yard)?

Answer 1

Given:

Two points A and B are on opposite sides of a building.

A surveyor chooses a third point C 73 yd from B and 101 yd from A, with angle C measuring 53.5°.

Required:

To find the distance between A and B.

Explanation:

Here,

$\begin{gathered} a=73 \\ b=101 \\ \angle C=53.5\degree \end{gathered}$

Let the distance between A and be c.

Now by cosine rule,

$c=\sqrt{a^2+b^2-2ab\cdot\cos C}$$=\sqrt{73^2+101^2-2(73)(101)\cdot\cos53.5}$$\begin{gathered} =\sqrt{5329+10201-8874.3643} \\ \\ c\approx82.21 \end{gathered}$

Final Answer:

The distance between A and B is 82.21 yards.