The angle of elevation of the top of a house from the bottom of a tower 160m high is 26.from the top of a tower the angle of elevation is 24.what is the height of the house if the tower and the height are 50m apart?
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To find the height of the house, we can use the concept of trigonometry, specifically tangent.
Let's denote the height of the house as 'h'. According to the given information, the height of the tower is 160m, and the distance between the tower and the house is 50m.
From the bottom of the tower, the angle of elevation to the top of the house is 26°. This means that the tangent of the angle can be used to relate the height of the house to the distance between the tower and the house:
tangent(26°) = h / 50
To find the height of the house, we need to isolate 'h' in the equation. We can do this by multiplying both sides of the equation by 50:
50 * tangent(26°) = h
Now, let's calculate this value using a scientific calculator:
50 * tangent(26°) ≈ 22.76
Therefore, the height of the house is approximately 22.76m.