A person is standing 25 meters away from a vertical cliff. If the angle of elevation to the top of the cliff is 60 degrees, what is the height of the cliff?
Practice Questions
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Q1
A person is standing 25 meters away from a vertical cliff. If the angle of elevation to the top of the cliff is 60 degrees, what is the height of the cliff?
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25 m
Using tan(60°) = height/25, we have √3 = height/25. Therefore, height = 25√3 ≈ 43.3 m.
Questions & Step-by-step Solutions
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Q
Q: A person is standing 25 meters away from a vertical cliff. If the angle of elevation to the top of the cliff is 60 degrees, what is the height of the cliff?
Solution: Using tan(60°) = height/25, we have √3 = height/25. Therefore, height = 25√3 ≈ 43.3 m.
Steps: 7
Step 1: Understand the problem. You have a person standing 25 meters away from a cliff and looking up at the top of the cliff at an angle of 60 degrees.
Step 2: Visualize the situation. Imagine a right triangle where one side is the height of the cliff, the other side is the distance from the person to the cliff (25 meters), and the angle between the ground and the line of sight to the top of the cliff is 60 degrees.
Step 3: Use the tangent function. In a right triangle, the tangent of an angle is equal to the opposite side (height of the cliff) divided by the adjacent side (distance from the person to the cliff). So, tan(60°) = height / 25.
Step 4: Find the value of tan(60°). The value of tan(60°) is √3.
Step 5: Set up the equation. Now, we can write the equation as √3 = height / 25.
Step 6: Solve for height. Multiply both sides of the equation by 25 to isolate height: height = 25 * √3.
Step 7: Calculate the height. Using a calculator, find the value of 25 * √3, which is approximately 43.3 meters.
