Problem

The angle of elevation from a point on the ground to the top of a pyramid is $21^{\circ} 10^{\prime}$. The angle of elevation from a point 168 feet farther back to the top of the pyramid is $11^{\circ} 20^{\prime}$. Find the height of the pyramid. What is the height of the pyramid? $\mathrm{ft}$ (Round to the nearest integer.)

Solution

Step 1 :Let's denote the height of the pyramid as h, the distance from the closer point on the ground to the pyramid as d, and the distance from the farther point on the ground to the pyramid as d+168.

Step 2 :From the definition of tangent, we have the following two equations: \(\tan(21°10′) = \frac{h}{d}\) and \(\tan(11°20′) = \frac{h}{d+168}\).

Step 3 :Solving these two equations, we find that d = 348.27 feet and h = 134.85 feet.

Step 4 :Rounding to the nearest integer, we find that the height of the pyramid is 135 feet.

Step 5 :Final Answer: The height of the pyramid is \(\boxed{135}\) feet.

From Solvely APP
Source: https://solvelyapp.com/problems/19383/

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