A person is standing on a hill 80 m high. The angle of depression to a car on the ground is 60 degrees. How far is the car from the base of the hill?
Practice Questions
1 question
Q1
A person is standing on a hill 80 m high. The angle of depression to a car on the ground is 60 degrees. How far is the car from the base of the hill?
40 m
80 m
20√3 m
40√3 m
Using tan(60°) = height/distance, we have distance = height/tan(60°) = 80/√3 = 40√3 m.
Questions & Step-by-step Solutions
1 item
Q
Q: A person is standing on a hill 80 m high. The angle of depression to a car on the ground is 60 degrees. How far is the car from the base of the hill?
Solution: Using tan(60°) = height/distance, we have distance = height/tan(60°) = 80/√3 = 40√3 m.
Steps: 11
Step 1: Understand the problem. A person is on a hill that is 80 meters high and sees a car on the ground at an angle of 60 degrees downwards.
Step 2: Visualize the situation. Draw a right triangle where the height of the hill is one side (80 m), the distance from the base of the hill to the car is the other side, and the line of sight to the car is the hypotenuse.
Step 3: Identify the relevant angle. The angle of depression from the person to the car is 60 degrees.
Step 4: Use the tangent function. In a right triangle, the tangent of an angle is the opposite side (height of the hill) divided by the adjacent side (distance to the car).
Step 5: Write the equation using the tangent function: tan(60°) = height / distance.
Step 6: Substitute the known values into the equation: tan(60°) = 80 / distance.
