Ameteorologist measures the angle of elevation of a weather balloon with the ground as 41. a radio signal from the balloon indicates that it is 1503 m from his location. to the nearest meter, how high above the ground in the balloon ?

Here you would use right triangle trig (SOH CAH TOA)
So first draw a right triangle. Imagine youre standing at the angle opposite the right angle which is the one on the ground.This angle is the 41°. Now Imagine the balloon is as the angle above the right triangle. Well since the balloon is 1503 m from his location this would be the hypotenuse. SInce we are trying to find the height (x) we would use sine since
sine = opposite/hypotenuse . Now lets solve make sure calculator is in degree mode:

sin41 = x/1503      multiply both sides by 1503 to cancel it out
1503sin41 = x        plug into calculator
x = 986.057 ft
The balloon is 986.057 feet above the ground.

In the right triangle the hypotenuse is the distance indicated by the radio signal, 1503 m, and the angle is 41°.

The opposed leg to 41° is the height of the ballon.

Then you can use the sine trigonometric function.

sine (41°) = opposed leg / hypotenuse = x / 1503 m => x = 1503m * sine(41°)

=> x = 986m.

986m