A person standing 20 meters away from a vertical cliff observes the top of the c
Practice Questions
Q1
A person standing 20 meters away from a vertical cliff observes the top of the cliff at an angle of elevation of 75 degrees. What is the height of the cliff?
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Questions & Step-by-Step Solutions
A person standing 20 meters away from a vertical cliff observes the top of the cliff at an angle of elevation of 75 degrees. What is the height of the cliff?
Step 1: Understand the problem. You have a person standing 20 meters away from a cliff and looking up at the top of the cliff at an angle of 75 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 of elevation is 75 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 problem, tan(75°) = height / 20.
Step 5: Rearrange the equation to find the height. Multiply both sides by 20: height = 20 * tan(75°).
Step 6: Calculate tan(75°). You can use a calculator to find that tan(75°) is approximately 3.732.
Step 7: Substitute the value of tan(75°) into the equation. So, height = 20 * 3.732.
Step 8: Perform the multiplication. Calculate 20 * 3.732 to get approximately 74.64 meters.
Step 9: Conclude that the height of the cliff is approximately 74.64 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 – The scenario can be visualized as a right triangle where the height of the cliff is the opposite side, the distance from the cliff is the adjacent side, and the angle of elevation is given.
