Problem

An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 28 feet up. The ladder makes an angle of $71^{\circ}$ with the ground. Find the length of the ladder. Round your answer to the nearest hundredth of a foot if necessary.

Solution

Step 1 :Given: angle = $71^\circ$, height = 28 feet

Step 2 :Convert angle to radians: angle_rad = $\frac{71 \times \pi}{180}$

Step 3 :Calculate sine of the angle: sin(angle_rad) = $\sin(1.239183768915974)$

Step 4 :Use sine function to find ladder length: ladder_length = $\frac{28}{\sin(1.239183768915974)}$

Step 5 :Calculate ladder length: ladder_length = 29.61337907322678

Step 6 :Round ladder length to the nearest hundredth: ladder_length_rounded = 29.61

Step 7 :\(\boxed{\text{Final Answer: The length of the ladder is approximately 29.61 feet.}}\)

From Solvely APP
Source: https://solvelyapp.com/problems/7410/

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