A person is standing 20 meters away from a vertical cliff. If the angle of eleva
Practice Questions
Q1
A person is standing 20 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?
10√3 m
20√3 m
30√3 m
40√3 m
Questions & Step-by-Step Solutions
A person is standing 20 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?
Step 1: Understand the problem. We have a person standing 20 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 (20 meters), and the angle between the ground and the line of sight to the top of the cliff is 60 degrees.
Step 3: Recall the tangent function. In a right triangle, the tangent of an angle is the ratio of the opposite side (height of the cliff) to the adjacent side (distance from the person to the cliff).
Step 4: Write the equation using the tangent function. For our angle of 60 degrees, we have: tan(60°) = height / 20.
Step 5: Find the value of tan(60°). The value of tan(60°) is √3.
Step 6: Substitute the value into the equation. Now we have: √3 = height / 20.
Step 7: Solve for the height. Multiply both sides by 20 to isolate height: height = 20 * √3.
Step 8: Calculate the height. The height of the cliff is 20√3 meters.
Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the cliff and the distance from the cliff.
Right Triangle Properties – Understanding the properties of right triangles is essential, as the scenario describes a right triangle formed by the height of the cliff, the distance from the cliff, and the line of sight.
