A mountain climber wants to determine the height, MN, of a mountain. He uses a theodolite (instrument used to measure angles). The mountain climber is standing on flat ground. P is in the same horizontal plane as the foot of the mountain N. He measures the following angles from P: The angle of elevation of the top of the mountain M, is x MPQ is y° He then walks d metres to point Q, which is also in the same horizontal plane as P and N, and measures POM which is z°. d sin x sin z 8.1 Show that: MN = sin (y+z) 8.2 Calculate MN, without using a calculator if d=1000 m, x= 90°-y and y=:.

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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.