A kite is flying at a height of 50 m. 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? (2020)
Practice Questions
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Q1
A kite is flying at a height of 50 m. 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? (2020)
50 m
70 m
100 m
30 m
Using tan(45) = 1, distance = height = 50 m.
Questions & Step-by-step Solutions
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Q
Q: A kite is flying at a height of 50 m. 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? (2020)
Solution: Using tan(45) = 1, distance = height = 50 m.
Steps: 8
Step 1: Understand that the height of the kite is 50 meters.
Step 2: Know that the angle of elevation from the ground to the kite is 45 degrees.
Step 3: Recall that the tangent of an angle in a right triangle is the ratio of the opposite side (height) to the adjacent side (distance from the point to the base of the kite).
Step 4: Use the formula: tan(angle) = opposite/adjacent.
Step 5: Substitute the values: tan(45 degrees) = height/distance.
Step 6: Since tan(45 degrees) equals 1, we have 1 = 50/distance.
Step 7: Rearrange the equation to find distance: distance = height.
Step 8: Therefore, the distance from the point on the ground to the base of the kite is 50 meters.
