Question

applying trigonometry to solve real-world miguel needs to fix a window screen that is 23 feet above the ground. the ladder he uses makes a 75° angle with the ground. what is the shortest possible length of the ladder if the top of it is 23 feet off the ground? round to the nearest whole number. 6 ft 22 ft 24 ft 89 ft

Explanation:

Step1: Define trigonometric relation

We use the sine function, where $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta=75^\circ$, opposite side = 23 ft (height of window), hypotenuse = ladder length $L$.

Step2: Rearrange to solve for $L$

$L = \frac{23}{\sin(75^\circ)}$

Step3: Calculate value

First, $\sin(75^\circ) \approx 0.9659$. Then $L \approx \frac{23}{0.9659} \approx 23.81$

Step4: Round to nearest whole number

$23.81$ rounds to 24.

Answer:

C. 24 ft