8. a 7.5 ft ladder is leaning against a wall so that the foot of the ladder is 2 ft 9 inches from the base…

8. a 7.5 ft ladder is leaning against a wall so that the foot of the ladder is 2 ft 9 inches from the base of the wall. what angle does the ladder make with the wall? hint: you will need to convert 2 ft 9 inches into feet.

8. a 7.5 ft ladder is leaning against a wall so that the foot of the ladder is 2 ft 9 inches from the base of the wall. what angle does the ladder make with the wall? hint: you will need to convert 2 ft 9 inches into feet.

Answer

Explanation:

Step1: Convert 2 ft 9 inches to feet

We know that 1 foot = 12 inches, so 9 inches = $\frac{9}{12}$ = 0.75 feet. Then 2 ft 9 inches = 2 + 0.75 = 2.75 feet.

Step2: Identify the triangle sides

The ladder length (hypotenuse) is 7.5 ft, the distance from the base (adjacent side to the angle with the wall) is 2.75 ft. We use cosine: $\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}$.

Step3: Calculate the cosine value

$\cos\theta = \frac{2.75}{7.5} \approx 0.3667$.

Step4: Find the angle

$\theta = \arccos(0.3667) \approx 69.9^\circ$ (using a calculator for arccos).

Answer:

The angle the ladder makes with the wall is approximately $\boldsymbol{70^\circ}$ (or more precisely around $69.9^\circ$).