From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the height of the hill is 100 m, how far is the point from the base of the hill?
Practice Questions
1 question
Q1
From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the height of the hill is 100 m, how far is the point from the base of the hill?
100 m
50 m
200 m
150 m
Using tan(45°) = height/distance, we have distance = height/tan(45°) = 100/1 = 100 m.
Questions & Step-by-step Solutions
1 item
Q
Q: From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the height of the hill is 100 m, how far is the point from the base of the hill?
Solution: Using tan(45°) = height/distance, we have distance = height/tan(45°) = 100/1 = 100 m.
Steps: 10
Step 1: Understand that the angle of elevation is the angle formed between the horizontal line from the point on the ground and the line of sight to the top of the hill.
Step 2: Identify that the height of the hill is given as 100 meters.
Step 3: Recognize that the angle of elevation is 45 degrees.
Step 4: Recall the trigonometric function tangent (tan), which relates the angle of a right triangle to the opposite side (height) and the adjacent side (distance).
Step 5: Write the formula for tangent: tan(angle) = opposite/adjacent.
Step 6: Substitute the known values into the formula: tan(45°) = height/distance.
Step 7: Since tan(45°) equals 1, rewrite the equation as 1 = 100/distance.
Step 8: Rearrange the equation to find distance: distance = height/tan(45°).
Step 9: Substitute the height into the equation: distance = 100/1.
Step 10: Calculate the distance: distance = 100 meters.
