Question

The altitude of the base of a cloud

formation is called the ceiling. To find the ceiling

one night, a meteorologist directed a spotlight

vertically at the clouds. Using a theodolite placed

83 meters from the spotlight and 1. 5 meters above

the ground, he found the angle of elevation to be

62. 7º. How high was the ceiling?

Answer 1

The height of the ceiling is 162.31 meters

The situation will form a right angle triangle.

Right angle triangle:

Right triangle has one of its angles as 90 degree. Therefore, the sides can be found using trigonometric ratios

The triangle formed, the theodolite distance from the spotlight is the  adjacent side. Therefore,

tan 62.7 = opposite / adjacent

tan 62.7 = x / 83

cross multiply

x = 83 × tan 62.7

x = 160.809554025 m

Therefore, the height of the ceiling form the ground is as follows:

• 160.809554025 + 1.5 = 162.309554025 m

learn more on right angle triangle here; https://brainly.com/question/13481976