Question

the proper angle for a ladder is about 75 degrees from the ground. suppose you have a 8 foot ladder. how far from the house should you place the base of the ladder? round to the hundredths. (2 decimal places) feet

Explanation:

Step1: Identify trigonometric ratio

We use cosine, since $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$, where the adjacent side is the distance from the house, and hypotenuse is the ladder length.

Step2: Plug in known values

$\cos(75^\circ) = \frac{x}{8}$, where $x$ is the distance from the house.

Step3: Solve for $x$

Rearrange to isolate $x$: $x = 8 \times \cos(75^\circ)$
Calculate $\cos(75^\circ) \approx 0.2588$, so $x \approx 8 \times 0.2588 = 2.0704$

Step4: Round to 2 decimal places

Round $2.0704$ to the nearest hundredth.

Answer:

2.07 feet