Hi could anybody help me how to find the angle of elevation pls.Trigonometry problem.

Question

To determine the cloud height at night, many small airport have a spot light that shines on the clouds. The angle the light beam makes with the ground is 70. An observer location on the ground 300m from the light, measure the angle of elevation of the point where the light shines on the clouds. Suppose the angle of elevation of this point is 60°, and the light and the observer are an oppoite sides of the point. Find the cloud height, to the nearest meter.

Thank you so much.

Answer 1

Draw and label a diagram

Draw a line from the cloud perpendicular to the ground

Label the line h (represents the height of the cloud)

Label the point on the ground g

The distance from g to the observer is d

The distance from g to the spot light is 300 - d

tan 60° = h / d

d tan 60° = h

d = h / tan 60°, equation A

tan 70° = h / (300 - d)

(300 - d) tan 70° = h

300 tan 70° - d tan 70° = h

300 tan 70° = h + d tan 70°

300 tan 70° - h = d tan 70°

(300 tan 70° - h) / tan 70° = d, equation B

Equate equatio A to equation B and solve for h.

Answer 2

have triangle 70,60,50 degrees and opposite 50 angle is side of 300.

law of sines, side opposite 70 degree angle is q=300*sin(70)/sin(50)

q is also the hypotenuse at observer to cloud. And where height is opposite

the 60 degree angle. height=h=sin(60)*q. Note sin(60)=(√3)/2

to nearest meter is h=319 meters