A kite is flying at a height of 30 meters. If the angle of elevation from a point on the ground to the kite is 45 degrees, how far is the point from the base of the kite?
Practice Questions
1 question
Q1
A kite is flying at a height of 30 meters. If the angle of elevation from a point on the ground to the kite is 45 degrees, how far is the point from the base of the kite?
15 m
30 m
45 m
60 m
Using tan(45°) = height/distance, we have 1 = 30/distance. Therefore, distance = 30 m.
Questions & Step-by-step Solutions
1 item
Q
Q: A kite is flying at a height of 30 meters. If the angle of elevation from a point on the ground to the kite is 45 degrees, how far is the point from the base of the kite?
Solution: Using tan(45°) = height/distance, we have 1 = 30/distance. Therefore, distance = 30 m.
Steps: 7
Step 1: Understand that the height of the kite is 30 meters.
Step 2: Know that the angle of elevation from the ground to the kite is 45 degrees.
Step 3: Recall the tangent function in a right triangle: tan(angle) = opposite/adjacent.
Step 4: In this case, the opposite side is the height of the kite (30 meters) and the adjacent side is the distance from the point on the ground to the base of the kite.
Step 5: Set up the equation using the tangent of 45 degrees: tan(45°) = height/distance.
Step 6: Since tan(45°) equals 1, we can write the equation as 1 = 30/distance.
Step 7: Rearrange the equation to find the distance: distance = 30 meters.
