Question

A. Jamie has a ladder that is 15 ft long. She wants to lean the ladder against a vertical wall so that the top of the ladder is 14 ft above the ground.

Draw a picture of the ladder leaning against the wall and label the lengths listed in the problem:



b. Use Trigonometry to find the angle formed between the ground and the ladder using your diagram and values from part 1a. Round to the nearest whole number. Show your work:


c. For safety reasons, Jamie wants the angle the ladder makes with the ground to be no greater than 75°. Will the ladder be safe the way she has it positioned?

Answer 1

B. ∠C = 69°

C. Jamie has positioned the ladder safely.

Explanation:

A. In the figure attached length of ladder AC = 15 ft

and the top of the ladder is at the point A 14 ft above the ground.

B. SinC =
`\frac{\text{Opposite side}}{\text{Hypotenuse}}`

=
`(14)/(15)`

`C=sin^(-1)((14)/(15) )`

C = 68.96°

C ≈ 69°

C). For safety reasons, angle between the ladder and the ground should be less than 75°.

Existing angle between the ladder and ground is 69° which is less than the angle required for safety.

Therefore, Jamie has positioned the ladder safely.