Question: A person is 25 meters away from a cliff. If the angle of elevation to the top of the cliff is 45 degrees, what is the height of the cliff?
Options:
25 meters
30 meters
35 meters
40 meters
Correct Answer: 25 meters
Solution:
Height = distance * tan(45) = 25 * 1 = 25 meters.
A person is 25 meters away from a cliff. If the angle of elevation to the top of
Practice Questions
Q1
A person is 25 meters away from a cliff. If the angle of elevation to the top of the cliff is 45 degrees, what is the height of the cliff?
25 meters
30 meters
35 meters
40 meters
Questions & Step-by-Step Solutions
A person is 25 meters away from a cliff. If the angle of elevation to the top of the cliff is 45 degrees, what is the height of the cliff?
Step 1: Understand the problem. You have a person standing 25 meters away from a cliff.
Step 2: Know that the angle of elevation to the top of the cliff is 45 degrees.
Step 3: Remember that the tangent (tan) of an angle in a right triangle is the ratio of the opposite side (height of the cliff) to the adjacent side (distance from the person to the cliff).
Step 4: For an angle of 45 degrees, the value of tan(45) is 1.
Step 5: Use the formula: Height = distance * tan(angle). Here, distance is 25 meters and angle is 45 degrees.
Step 6: Substitute the values into the formula: Height = 25 * tan(45).
Step 7: Calculate: Height = 25 * 1 = 25 meters.
Step 8: Conclude that the height of the cliff is 25 meters.
Trigonometry – Understanding the relationship between angles and sides in right triangles, specifically using the tangent function.
Angle of Elevation – The angle formed by the horizontal line and the line of sight to an object above the horizontal.
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