A meteorologist measures the angle of elevation of a weather balloon as 41°. A radio signal from the balloon indicates that it is 1,503 meters from his location. To the nearest meter, how high above the ground is the balloon?
A. 986 m
B. 1,134 m
C. 1,307
D. 2,291
To solve this problem, we can use trigonometry.
We can use the tangent function to find the height of the balloon.
tangent(angle of elevation) = (height of balloon) / (distance from observer to balloon)
tan(41°) = (height of balloon) / (1,503 meters)
Using a calculator, we can find that tan(41°) ≈ 0.869
0.869 = (height of balloon) / (1,503 meters)
Multiplying both sides of the equation by 1,503 meters, we get:
1,303.207 = height of balloon
Rounding to the nearest meter, the height of the balloon is 1,303 meters.
Therefore, the answer is C. 1,307 meters