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A tower is 100 meters high. From a point 80 meters away from the base of the tow
A tower is 100 meters high. From a point 80 meters away from the base of the tower, what is the angle of elevation to the top of the tower?
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A tower is 100 meters high. From a point 80 meters away from the base of the tower, what is the angle of elevation to the top of the tower?
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tan(θ) = height/distance = 100/80, θ = tan⁻¹(1.25) ≈ 51.34 degrees.
Questions & Step-by-step Solutions
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Q
Q: A tower is 100 meters high. From a point 80 meters away from the base of the tower, what is the angle of elevation to the top of the tower?
Solution:
tan(θ) = height/distance = 100/80, θ = tan⁻¹(1.25) ≈ 51.34 degrees.
Steps: 7
Show Steps
Step 1: Identify the height of the tower, which is 100 meters.
Step 2: Identify the distance from the point to the base of the tower, which is 80 meters.
Step 3: Use the formula for the tangent of the angle of elevation: tan(θ) = height/distance.
Step 4: Substitute the values into the formula: tan(θ) = 100/80.
Step 5: Simplify the fraction: 100/80 = 1.25.
Step 6: To find the angle θ, use the inverse tangent function: θ = tan⁻¹(1.25).
Step 7: Calculate θ using a calculator: θ ≈ 51.34 degrees.
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