A person standing on the ground observes the top of a pole at an angle of elevat
Practice Questions
Q1
A person standing on the ground observes the top of a pole at an angle of elevation of 75 degrees. If the pole is 10 m high, how far is the person from the base of the pole? (2023)
2.68 m
5.77 m
10 m
15 m
Questions & Step-by-Step Solutions
A person standing on the ground observes the top of a pole at an angle of elevation of 75 degrees. If the pole is 10 m high, how far is the person from the base of the pole? (2023)
Step 1: Understand the problem. We have a pole that is 10 meters high and we want to find out how far a person is from the base of the pole.
Step 2: Identify the angle of elevation. The person sees the top of the pole at an angle of 75 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 pole) divided by the adjacent side (distance from the pole).
Step 4: Write the formula. We can express this as: tan(angle) = height / distance.
Step 5: Rearrange the formula to find distance. This gives us: distance = height / tan(angle).
Step 6: Plug in the values. Here, height = 10 m and angle = 75 degrees, so we calculate: distance = 10 / tan(75).
Step 7: Calculate tan(75 degrees). The value of tan(75 degrees) is approximately 3.732.
Step 8: Perform the division. Now calculate: distance = 10 / 3.732.
Step 9: Get the final answer. This gives us approximately 2.68 meters.
Trigonometry – The question tests the understanding of right triangle relationships, specifically using the tangent function to relate angles and side lengths.
Angle of Elevation – The concept of angle of elevation is crucial for determining the relationship between the observer's position and the height of the pole.
Height and Distance Calculation – The problem involves calculating the horizontal distance from the pole using the height and the angle of elevation.
