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 20 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 20 m, how far is the point from the base of the hill?
20 m
10 m
30 m
40 m
Using tan(45°) = height/distance, we have 1 = 20/distance. Therefore, distance = 20 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 20 m, how far is the point from the base of the hill?
Solution: Using tan(45°) = height/distance, we have 1 = 20/distance. Therefore, distance = 20 m.
Steps: 9
Step 1: Understand that the angle of elevation is the angle formed between the horizontal ground and the line of sight to the top of the hill.
Step 2: Identify that the height of the hill is 20 meters.
Step 3: Recognize that the angle of elevation is 45 degrees.
Step 4: Recall the tangent function in trigonometry, which is defined as tan(angle) = opposite/adjacent.
Step 5: In this scenario, the 'opposite' side is the height of the hill (20 m) and the 'adjacent' side is the distance from the point to the base of the hill.
Step 6: Set up the equation using the tangent of 45 degrees: tan(45°) = height/distance.
Step 7: Substitute the known values into the equation: tan(45°) = 20/distance.
Step 8: Since tan(45°) equals 1, rewrite the equation as 1 = 20/distance.
Step 9: Solve for distance by rearranging the equation: distance = 20 m.
