Final answer:
To find the length of the ladder, use the sine function based on the given angle of elevation and the height from the ground. After calculating, round the length of the ladder to the nearest tenth.
Step-by-step explanation:
The student is asking how to find the length of a ladder that is leaning against a house with a given angle of elevation and height from the ground. To solve this problem, we can use trigonometry, specifically the sine function, since we have the angle of elevation and the opposite side of the right triangle formed by the ladder, the wall, and the ground. The formula we use is sin(\theta) = opposite/hypotenuse, where \(\theta\) is the angle of elevation, the opposite side is the height from the ground to the top of the ladder, and the hypotenuse is the length of the ladder we want to find.
Step-by-step solution:
- Identify the known values: angle \(\theta\) is 71 degrees, and the opposite side is 14 feet.
- Apply the sine function: sin(71 degrees) = 14/ladder length.
- Solve for ladder length: ladder length = 14/sin(71 degrees).
- Use a calculator to find the sine value and solve the equation.
- Round the result to the nearest tenth.
After performing the calculations, we determine the length of the ladder, rounded to the nearest tenth.