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#trigonometry
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The angle of elevation of a building from a measuring instrument placed on the ground is 30°.if the building is 40m high, how far is the instrument from the foot of the building?
Israel Oladotun
Jan 13
The angle of elevation of a building from a measuring instrument placed on the ground is 30°.if the building is 40m high, how far is the instrument from the foot of the building?
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Jan 13
Let x be the distance from the instrument to the foot of the building.
We can use the tangent function to solve this problem.
The tangent of the angle of elevation is equal to the opposite side (40m) divided by the adjacent side (x).
So, tan(30°) = 40m / x.
Using the tangent of 30°, which is 1/√3, we can rewrite the equation as:
1/√3 = 40m / x.
Cross-multiplying, we get:
x = 40m * √3.
x = 40√3 m.
Therefore, the instrument is approximately 69.28m from the foot of the building. Answer: \boxed{69.28}.
We can use the tangent function to solve this problem.
The tangent of the angle of elevation is equal to the opposite side (40m) divided by the adjacent side (x).
So, tan(30°) = 40m / x.
Using the tangent of 30°, which is 1/√3, we can rewrite the equation as:
1/√3 = 40m / x.
Cross-multiplying, we get:
x = 40m * √3.
x = 40√3 m.
Therefore, the instrument is approximately 69.28m from the foot of the building. Answer: \boxed{69.28}.
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