From the top of a hill, the angle of depression to a car parked on the ground is 45 degrees. If the height of the hill is 100 meters, how far is the car from the base of the hill?
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From the top of a hill, the angle of depression to a car parked on the ground is 45 degrees. If the height of the hill is 100 meters, how far is the car from the base of the hill?
Q: From the top of a hill, the angle of depression to a car parked on the ground is 45 degrees. If the height of the hill is 100 meters, how far is the car from the base of the hill?
Step 1: Understand the problem. We have a hill that is 100 meters tall.
Step 2: The angle of depression from the top of the hill to the car is 45 degrees.
Step 3: Visualize the situation. Draw a right triangle where the height of the hill is one side (100 meters) and the distance from the base of the hill to the car is the other side.
Step 4: Recall the definition of the angle of depression. It is the angle formed between the horizontal line from the top of the hill and the line of sight to the car.
Step 5: Since the angle of depression is 45 degrees, the angle at the base of the triangle (where the car is) is also 45 degrees because of alternate interior angles.
Step 6: Use the tangent function. The tangent of an angle in a right triangle is the opposite side (height of the hill) divided by the adjacent side (distance from the base of the hill to the car).
