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The angle of elevation of the top of a building from the foot of a tower is 70° and the angle of elevation of the top of the tower from the foot of the building is 40°. Find the height of the building if the tower is 50 m tall.

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Xero099idn

The height of the building located at a distance from the tower is approximately 163.716 meters.

How to determine the height of a building

After a careful reading to the statement, we represent all the information given in a geometric diagram. In this question we must apply trigonometric relationships to calculate the height of the building (h), in meters, based on the fact of the existing two right triangles. The diagram is presented in the image attached below.

Now we proceed to calculate the height of the building:

[tex]h = \left(\frac{50\,m}{\tan 40^{\circ}} \right)\cdot \tan 70^{\circ}[/tex]

h ≈ 163.716 m

The height of the building located at a distance from the tower is approximately 163.716 meters. [tex]\blacksquare[/tex]

To learn more on trigonometric relationships, we kindly invite to check this verified question: https://brainly.com/question/6904750

View image Xero099
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