Question

Two points, a and b, are on opposite sides of a building. a surveyor chooses a third point, c, 80 yd from b and 104 yd from a, with angle acb measuring 51.2°. how far apart are a and b (to the nearest yard)?

Answer 1

The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. The distance between A and B is 85.6 yds.

The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. It is given by the formula,

$c=\sqrt{a^{2}+ b^{2}-2ab.cos \theta }$

where

c is the third side of the triangle

a and b are the other two sides of the triangle,

and θ is the angle opposite to the third side, therefore, opposite to side c.

The three points A, B, and C will form a triangle. Therefore, using the law of cosine the measure of the third side AB can be written as,

$AB=\sqrt{(AC)^{2}+(B C)^{2} -2(AC)(BC).Cos(51.2)^{o} }$

$AB=\sqrt{(80)^{2}+(104)^{2} -2(80)(104).Cos(51.2)^{o} }$

$AB=\sqrt{6400+10816 -16640.Cos(51.2)^{o} }$

$AB=\sqrt{7328.4}$

AB = 25.6 yd

Hence, the distance between A and B is 85.6 yds.

Learn more about the Law of Cosine:

brainly.com/question/17289163

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