A person is standing on a hill that is 80 meters high. If the angle of depressio
Practice Questions
Q1
A person is standing on a hill that is 80 meters high. If the angle of depression to a point on the ground is 45 degrees, how far is the point from the base of the hill?
80 m
40 m
80√2 m
40√2 m
Questions & Step-by-Step Solutions
A person is standing on a hill that is 80 meters high. If the angle of depression to a point on the ground is 45 degrees, how far is the point from the base of the hill?
Step 1: Understand that the height of the hill is 80 meters.
Step 2: Know that the angle of depression is 45 degrees.
Step 3: Recognize that the angle of depression creates a right triangle with the height of the hill and the distance to the point on the ground.
Step 4: Use the tangent function, which relates the angle to the opposite side (height) and the adjacent side (distance).
Step 5: Write the formula: tan(angle) = height/distance.
Step 6: Substitute the values into the formula: tan(45°) = height/distance.
Step 7: Since tan(45°) equals 1, the equation becomes 1 = 80/distance.
Step 8: Rearrange the equation to find distance: distance = height/tan(45°).
Step 9: Substitute the height: distance = 80/1.
Step 10: Calculate the distance: distance = 80 meters.
Trigonometry – The problem involves using the tangent function to relate the height of the hill to the distance from the base using the angle of depression.
Angle of Depression – Understanding that the angle of depression from the top of the hill to the point on the ground is equal to the angle of elevation from the point on the ground to the top of the hill.
