Question
A right triangle is formed by a ladder resting against a wall. The ladder is 20 feet long, and the top if the ladder rests 19 ft up the height of the wall. Find the approximate angle formed where the top of the ladder rests against the wall.
71.8 degrees
43.5 degrees
90 degrees
18.2 degrees
71.8 degrees
43.5 degrees
90 degrees
18.2 degrees
Answers
GPT-4o mini
To find the angle formed where the top of the ladder rests against the wall, we can use trigonometric functions. Specifically, we will use the sine function, which is defined as:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
In this case:
- The "opposite" side is the height at which the ladder touches the wall, which is 19 ft.
- The "hypotenuse" is the length of the ladder, which is 20 ft.
We can find the angle \(\theta\) using the inverse sine function:
\[
\theta = \sin^{-1}\left(\frac{19}{20}\right)
\]
Calculating \(\frac{19}{20}\):
\[
\frac{19}{20} = 0.95
\]
Now, we compute \(\theta\):
\[
\theta = \sin^{-1}(0.95) \approx 71.8 \text{ degrees}
\]
Thus, the angle formed where the top of the ladder rests against the wall is approximately **71.8 degrees**.
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
In this case:
- The "opposite" side is the height at which the ladder touches the wall, which is 19 ft.
- The "hypotenuse" is the length of the ladder, which is 20 ft.
We can find the angle \(\theta\) using the inverse sine function:
\[
\theta = \sin^{-1}\left(\frac{19}{20}\right)
\]
Calculating \(\frac{19}{20}\):
\[
\frac{19}{20} = 0.95
\]
Now, we compute \(\theta\):
\[
\theta = \sin^{-1}(0.95) \approx 71.8 \text{ degrees}
\]
Thus, the angle formed where the top of the ladder rests against the wall is approximately **71.8 degrees**.