Question

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.

1A. Use trigonometry to find the angle formed between the ground and the ladder. Round to the nearest whole number

2A. For safety reasons Jamie wants the angle the ladder makes with the ground to be no greater than 75 degrees. Will the ladder be safe the way she has it positioned?

Answer 1

1A. = 68.96 degrees.

2A. = YES

Explanation:

Hi, to answer this question we have to apply:

sin (angle ) = opposite side / hypotenuse

Since the triangle formed is a right triangle ( see attachment), the hypotenuse is the length of the ladder (the longest side), and the opposite side to the angle is the distance between the top of ladder and the ground.

Replacing with the value given

sin x = 14/15

Solving for x

x = arcsin 14/15

x = 68.96 degrees. (1A)

Since the angle is lower than 75 degrees, the ladder is safe the way is positioned.