Question

A 65 ft. long swimming pool is to be constructed. The pool will be 4 ft. deep at one end and 11 ft. deep at the other. To the nearest degree, what will be the measure of the acute angle the bottom of the pool makes with the wall at the deep end

Answer 1

Measure of the acute angle = 84°

Explanation:

In the figure attached,

ABDE is a swimming pool having length 'AB' = 65 feet

Depth of one end of the pool is BE = 4 feet

And depth of the other end AD = 11 feet

Acute angle between the bottom of the pool (DE) and wall of the deep end (AD) is ∠ADE.

Now from ΔCDE,

tanx =
`(EC)/(DC)`

tanx =
`(7)/(65)`

x =
`\text{tan}^(-1)((7)/(65))`

x = 6.15°

Now measure of acute angle the bottom of the pool makes with wall at he deep end,

m∠ADE = (90 - 6.15)°

= 83.85°

≈ 84°