Question 13 A fireman's ladder leaning against a house makes an angle of 9 degrees with the ground. How long is the ladder if the bottom of the ladder is 56 feet from the base of the house? Round your answer to the nearest hundredth if necessary. The ladder is $$ \approx \square $$ feet long. Submit Question

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UpStudy AI · Accepted Answer

**Step 1.** Draw a right triangle where the ladder is the hypotenuse ($$L$$), the distance from the house is the adjacent side ($$56$$ feet), and the angle between the ladder and the ground is $$9^\circ$$.

**Step 2.** Use the cosine function, which relates the adjacent side to the hypotenuse:
$$
\cos 9^\circ = \frac{56}{L}
$$

**Step 3.** Solve for $$L$$ by rearranging the equation:
$$
L = \frac{56}{\cos 9^\circ}
$$

**Step 4.** Evaluate the cosine:
$$
\cos 9^\circ \approx 0.98769
$$

**Step 5.** Substitute and compute:
$$
L \approx \frac{56}{0.98769} \approx 56.67
$$

**Step 6.** Therefore, the length of the ladder is:
$$
\approx 56.67 \text{ feet}
$$
The ladder is approximately 56.67 feet long.

Question 13
A fireman’s ladder leaning against a house makes an angle of
9 degrees with the ground. How long is the ladder if the
bottom of the ladder is 56 feet from the base of the house?
Round your answer to the nearest hundredth if necessary.
The ladder is feet long.
Submit Question

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Question 13 A fireman’s ladder leaning against a house makes an angle of 9 degrees with the ground. How long is the ladder if the bottom of the ladder is 56 feet from the base of the house? Round your answer to the nearest hundredth if necessary. The ladder is feet long. Submit Question