Question

Using his telescope, Tory watches a cheetah as it sits on the top of a cliff. The telescope is positioned so that the line of sight to the cheetah forms a 25° angle of elevation. The telescope sits 2.9 m above the ground and the base of the telescope is 134 m from the base of the cliff. To the nearest tenth of a meter, how high above the ground is the cheetah? If the answer does not have a tenths place then include a zero so that it does.

Answer 1

• 61.5 meters

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We know that the angle of elevation is 25° and the distance from the telescope to the base of the cliff is 134 m. Let's call the height of the cheetah h.

We can use the tangent function, which is opposite over adjacent, to set up an equation:

• tan(25°) = h/134 ⇒ h = 134 * tan(25°) ≈ 58.6 meters (use calculator)

Add the height of the telescope above the ground, which is 2.9 meters:

• 58.6 + 2.9 = 61.5 meters

So, the cheetah is approximately 61.5 meters above the ground.