A tower is 100 meters high. From a point 80 meters away from the base of the tow

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Question: 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?

Options:

45 degrees
60 degrees
30 degrees
75 degrees

Correct Answer: 60 degrees

Solution:

tan(θ) = height/distance = 100/80, θ = tan⁻¹(1.25) ≈ 51.34 degrees.

A tower is 100 meters high. From a point 80 meters away from the base of the tow

Practice Questions

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?

45 degrees
60 degrees
30 degrees
75 degrees

Questions & Step-by-Step Solutions

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?

Correct Answer: 51.34 degrees

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.

Trigonometry – The problem involves using the tangent function to find the angle of elevation based on the height of the tower and the distance from the observer.
Right Triangle Properties – Understanding the relationship between the sides of a right triangle and the angles formed, specifically in the context of elevation.

A tower is 100 meters high. From a point 80 meters away from the base of the tow

What’s inside this PDF?

A tower is 100 meters high. From a point 80 meters away from the base of the tow

Practice Questions

Questions & Step-by-Step Solutions

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