Question

A person is looking at the top of the tower, the angle of elevation from person’s eye
to the tower is 21.4 degree. Then the person moved 85.3 m farther from the tower and
the angle of elevation to the top of the tower from the new location is 16.7 degree.
Find the height of the tower.

Answer 1

Answer: person moved 85.3 m farther from the tower and

the angle of elevation to the top of the tower from the new location is 16.7 degree.

Find the height of the tower.

Answer 2

Answer:

The height of the tower is approximately 56.8 meters.

Step-by-step explanation:

Let the height of the tower be h, and let the distance between the person's original location and the tower be x.

From the first observation, we can see that:

tan(21.4°) = h/x

From the second observation, we can see that the person has moved 85.3m farther away from the tower, so the distance between the person's new location and the tower is x + 85.3. We also know that the angle of elevation has changed to 16.7°. Using the same formula as before, we get:

tan(16.7°) = h/(x + 85.3)

We now have two equations and two unknowns (h and x), so we can solve for h. Rearranging the first equation, we get:

x = h/tan(21.4°)

Substituting this expression for x into the second equation, we get:

tan(16.7°) = h/(h/tan(21.4°) + 85.3)

Simplifying this equation, we get:

tan(16.7°) = h/(h/tan(21.4°) + 85.3)

tan(16.7°) = tan(21.4°)/(h/x + 85.3)

tan(16.7°) = tan(21.4°)/(h/(h/tan(21.4°)) + 85.3)

tan(16.7°) = tan(21.4°)/(1/tan(21.4°) + 85.3/h)

Multiplying both sides by (1/tan(21.4°) + 85.3/h), we get:

h = tan(21.4°) * (85.3/(tan(16.7°) - tan(21.4°)))

Hence, we get:

h ≈ 56.8 m

Therefore, the height of the tower is approximately 56.8 meters.

To learn more about height: https://brainly.in/question/2272582

To learn more about angle of elevation: https://brainly.in/question/41511094

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