From a point on the ground, the angle of elevation of the top of a hill is 30 degrees. If the height of the hill is 50 meters, 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 of the top of a hill is 30 degrees. If the height of the hill is 50 meters, how far is the point from the base of the hill?
50 m
75 m
100 m
125 m
Using tan(30°) = height/distance, we have 1/√3 = 50/distance. Therefore, distance = 50√3 ≈ 86.6 m.
Questions & Step-by-step Solutions
1 item
Q
Q: From a point on the ground, the angle of elevation of the top of a hill is 30 degrees. If the height of the hill is 50 meters, how far is the point from the base of the hill?
Solution: Using tan(30°) = height/distance, we have 1/√3 = 50/distance. Therefore, distance = 50√3 ≈ 86.6 m.
Steps: 9
Step 1: Understand the problem. We have a hill that is 50 meters tall, and we want to find out how far away we are from the base of the hill when we look up at it at an angle of 30 degrees.
Step 2: Recall the relationship between the angle of elevation, height, and distance. We can use the tangent function, which is defined as the opposite side (height of the hill) over the adjacent side (distance from the base).
Step 3: Write down the formula for tangent: tan(angle) = height / distance.
Step 4: Substitute the known values into the formula. We have tan(30°) = height (50 meters) / distance.
Step 5: Find the value of tan(30°). It is equal to 1/√3.
Step 6: Set up the equation: 1/√3 = 50 / distance.
Step 7: Rearrange the equation to solve for distance: distance = 50 * √3.
Step 8: Calculate the distance. Using a calculator, 50 * √3 is approximately 86.6 meters.
Step 9: Conclude that the point is about 86.6 meters away from the base of the hill.
