Question

shown. A 12 foot ladder is leaning against a house to form angle x. The distance between the house and the bottom of the ladder is 4 feet. The angle between the house and the ground is 90 degrees. What is the value of x, rounded to the nearest degree? x ≈ ° According to the manufacturer, if the angle the ladder forms with the ground, x, is between 70° and 75°, then it meets safety standards. Is this ladder being used safely?

Answer 1

Part A

71°

Part B

The ladder is been used safely

Explanation:

Part A

We solve the above question using Trigonometric function of Cosine

cos x = Adjacent/Hypotenuse

Adjacent = The distance between the house and the bottom of the ladder = 4 feet

Hypotenuse = Length of the ladder = 12 feet

x = Angle

Hence:

cos x = 4/12

cos x = 1/3

x = arc cos (1/3)

x = 70.528779366°

Approximately to the nearest degree

= 71°

Part B

According to the manufacturer, if the angle the ladder forms with the ground, x, is between 70° and 75°, then it meets safety standards. Is this ladder being used safely?

Angle x = 71°

Therefore, the ladder is been used safely