An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 22 feet up. The ladder makes an angle of 66^(@) with the ground. Find the length of the ladder. Round your answer to the nearest tenth of a foot if necessary.

Identify Triangle Relationship: Identify the relationship between the ladder, the wall, and the ground to form a right triangle. The ladder acts as the hypotenuse (c), the height of the electric box above the ground represents the opposite side (a), and the distance from the base of the wall to the base of the ladder represents the adjacent side (b). We will use the sine function to find the length of the ladder.Use Sine Function: Use the sine function to relate the angle, the height of the electric box, and the length of the ladder. The sine of an angle in a right triangle is equal to the opposite side divided by the hypotenuse. So, sin(66°) = opposite/hypotenuse = 22/c.Calculate Ladder Length: Calculate the length of the ladder using the sine function. sin(66°) = 22/c c = 22 / sin(66°)Find Ladder Length: Use a calculator to find the value of sin(66°) and then divide 22 by this value to find the length of the ladder. sin(66°) ≈ 0.9135 (rounded to four decimal places) c ≈ 22 / 0.9135 c ≈ 24.1 feet (rounded to the nearest tenth)

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An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box $22$ feet up. The ladder makes an angle of $66^\circ$ with the ground. Find the length of the ladder. Round your answer to the nearest tenth of a foot if necessary.

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Q. An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box

22

feet up. The ladder makes an angle of

66^\circ

with the ground. Find the length of the ladder. Round your answer to the nearest tenth of a foot if necessary.

Identify Triangle Relationship: Identify the relationship between the ladder, the wall, and the ground to form a right triangle. $\newline$ The ladder acts as the hypotenuse $c$ , the height of the electric box above the ground represents the opposite side $a$ , and the distance from the base of the wall to the base of the ladder represents the adjacent side $b$ . We will use the sine function to find the length of the ladder.
Use Sine Function: Use the sine function to relate the angle, the height of the electric box, and the length of the ladder. $\newline$ The sine of an angle in a right triangle is equal to the opposite side divided by the hypotenuse. So, $\sin(66^\circ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{22}{c}$ .
Calculate Ladder Length: Calculate the length of the ladder using the sine function. $\sin(66^\circ) = \frac{22}{c}$ $c = \frac{22}{\sin(66^\circ)}$
Find Ladder Length: Use a calculator to find the value of $\sin(66°)$ and then divide $22$ by this value to find the length of the ladder. $\newline$ $\sin(66°) \approx 0.9135$ (rounded to four decimal places) $\newline$ $c \approx 22 / 0.9135$ $\newline$ $c \approx 24.1$ feet (rounded to the nearest tenth)