Question

A balloon attached to an atmospheric data-gathering device must be at least 1000 m high to begin recording information. Two spotters, Mary and Nathan, walk the same distance from the launch site at an angle of 70° to each other until they are 225 m apart. From these positions, they watch the rise of the balloon with instruments that record the angle of elevation. What angles of elevation must the instruments record in order for the balloon to be at the correct height for atmospheric data gathering?

Answer 1

The angle of elevation that the instruments have to record to be at the correct height is given as 79°

How to solve for the angle of elevation

We have 2x + 70 = 180

We have to find the value of x

2x = 110

x = 55

y/sin x = 225/sin70

This is the use of sine rule

From here we would have

y = 225(sinx/sin70)

Remember x = 55

y =  225(sin55/sin70)

y = 196.1378

tanθ = 1000/y

tan θ = 1000/196.1378

tanθ = 5.098

θ = tan⁻¹5.098

= 78.90°

Hence the conclusion is that the angle of elevation has to be 78.9 degrees for it to be at the correct height.

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