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.
Let's assume that the meteorologist is standing at point A and the weather balloon is at point B. The angle of elevation is the angle between the line from the meteorologist to the balloon and the horizontal ground.
First, we need to find the length of AB, which represents the height above the ground that we are looking for. We have the length of the side adjacent to the angle of elevation (AB) and we need to find the length of the side opposite to the angle of elevation (BC).
Since we have the length of AB (1,503 meters) and the angle of elevation (41 degrees), we can use the trigonometric function tangent (tan) to find the length of BC.
The tangent of an angle is the ratio of the opposite side length to the adjacent side length.
tan(41 degrees) = BC/1,503
To find BC, we rearrange the equation:
BC = tan(41 degrees) * 1,503
Using a calculator, we find:
BC ≈ 1,134 meters
Therefore, to the nearest meter, the balloon is approximately 1,134 meters above the ground.
The correct answer is B. 1,134 m.