Two points, A and B, are on opposite sides of a building. A surveyor chooses a third point, C, 79 yards from B and 105 yards from A, with angle ACB measuring 59.8°. How far apart are A and B to the nearest yard?
Ratios
A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.
Trigonometric Ratios
Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
As here we are given the length of AC, BC and the angle ACB so, we will use cosine rule to determine the distance between A and B.
Cosine rule :
c2 = a2 + b2 − 2ab cos(C)
where,
C is the angle ACB,
a is the length of BC,
b is the length of AC,
c is the length of AB.
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