If the angle of elevation from a point on the ground to the top of a hill is 30

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What’s inside this PDF?

Question: If the angle of elevation from a point on the ground to the top of a hill is 30 degrees and the distance from the point to the base of the hill is 20 meters, what is the height of the hill?

Options:

10√3 meters
20 meters
15 meters
5√3 meters

Correct Answer: 10√3 meters

Solution:

Using tan(30) = height / 20, height = 20 * tan(30) = 20 * (1/√3) = 20/√3 = 10√3 meters.

If the angle of elevation from a point on the ground to the top of a hill is 30

Practice Questions

If the angle of elevation from a point on the ground to the top of a hill is 30 degrees and the distance from the point to the base of the hill is 20 meters, what is the height of the hill?

10√3 meters
20 meters
15 meters
5√3 meters

Questions & Step-by-Step Solutions

If the angle of elevation from a point on the ground to the top of a hill is 30 degrees and the distance from the point to the base of the hill is 20 meters, what is the height of the hill?

Step 1: Understand that the angle of elevation is the angle formed between the ground and the line of sight to the top of the hill.
Step 2: Identify the given information: the angle of elevation is 30 degrees and the distance from the point to the base of the hill is 20 meters.
Step 3: Recall the tangent function in trigonometry, which relates the angle of elevation to the height of the hill and the distance from the point to the base of the hill. The formula is: tan(angle) = height / distance.
Step 4: Substitute the known values into the formula: tan(30 degrees) = height / 20 meters.
Step 5: Calculate tan(30 degrees). It is equal to 1/√3.
Step 6: Rewrite the equation using the value of tan(30): 1/√3 = height / 20.
Step 7: To find the height, multiply both sides of the equation by 20: height = 20 * (1/√3).
Step 8: Simplify the expression: height = 20/√3.
Step 9: To make it easier to understand, multiply the numerator and denominator by √3: height = (20√3)/3.
Step 10: The final height of the hill is approximately 10√3 meters.

Trigonometry – The problem tests the understanding of the tangent function in right triangles, specifically how to relate angles and side lengths.
Angle of Elevation – The concept of angle of elevation is crucial for determining the height of an object based on a horizontal distance.

If the angle of elevation from a point on the ground to the top of a hill is 30

What’s inside this PDF?

If the angle of elevation from a point on the ground to the top of a hill is 30

Practice Questions

Questions & Step-by-Step Solutions

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