Show your complete solutions by creating a diagram that represents the situation and coming up with a solution for each. 1. To measure the height of the cloud cover at an airport, a worker shines a spotlight upward at an angle 75° from the horizontal. An observer 600 m away measures the angle of elevation to the spot of light to be 45°. Find the height h of the cloud cover.
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.
Show your complete solutions by creating a diagram that represents the situation and coming up with a solution for each.
1. To measure the height of the cloud cover at an airport, a worker shines a spotlight upward at an angle 75° from the horizontal. An observer 600 m away measures the angle of elevation to the spot of light to be 45°. Find the height h of the cloud cover.
2. A 600-ft guy wire is attached to the top of a communications tower. If the wire makes an angle of 65° with the
ground, how tall is the communications tower?
3. To measure the height of an inaccessible cliff on the opposite side of a river, a surveyor makes the measurements shown in the figure at the right. Find the height of the cliff.
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