If you have a 16-ft extension ladder, and you place it against a wall so that it has a 35-degree angle of elevation, how high will the ladder reach on the wall? Round your answer to the nearest tenth of a foot.
If you have a 16-ft extension ladder, and you place it against a wall so that it has a 35-degree angle of elevation, how high will the ladder reach on the wall? Round your answer to the nearest tenth of a foot.
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
Question
![**Problem Statement:**
If you have a 16-ft extension ladder, and you place it against a wall so that it has a 35-degree angle of elevation, how high will the ladder reach on the wall?
Round your answer to the nearest tenth of a foot.
**Solution:**
To solve this problem, we will use trigonometry, specifically the sine function, which relates the angle of elevation to the height reached on the wall.
1. Define the variables:
- Length of the ladder (hypotenuse of the triangle): \( 16 \text{ ft} \)
- Angle of elevation: \( 35^\circ \)
- Height reached on the wall (opposite side of the triangle): \( h \)
2. Use the sine function:
\[
\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
3. Plug in the known values:
\[
\sin(35^\circ) = \frac{h}{16}
\]
4. Solve for \( h \):
\[
h = 16 \times \sin(35^\circ)
\]
5. Calculate the sine of 35 degrees (using a calculator or sine table):
\[
\sin(35^\circ) \approx 0.5736
\]
6. Substitute the value back into the equation:
\[
h = 16 \times 0.5736 \approx 9.2 \text{ ft}
\]
Thus, the ladder will reach approximately 9.2 feet high on the wall.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd24861ef-92b0-4cd8-8c54-2ac2200498ec%2Fb412eff7-70b9-4951-8c52-fbb3444632bc%2Fa67ldau_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
If you have a 16-ft extension ladder, and you place it against a wall so that it has a 35-degree angle of elevation, how high will the ladder reach on the wall?
Round your answer to the nearest tenth of a foot.
**Solution:**
To solve this problem, we will use trigonometry, specifically the sine function, which relates the angle of elevation to the height reached on the wall.
1. Define the variables:
- Length of the ladder (hypotenuse of the triangle): \( 16 \text{ ft} \)
- Angle of elevation: \( 35^\circ \)
- Height reached on the wall (opposite side of the triangle): \( h \)
2. Use the sine function:
\[
\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
3. Plug in the known values:
\[
\sin(35^\circ) = \frac{h}{16}
\]
4. Solve for \( h \):
\[
h = 16 \times \sin(35^\circ)
\]
5. Calculate the sine of 35 degrees (using a calculator or sine table):
\[
\sin(35^\circ) \approx 0.5736
\]
6. Substitute the value back into the equation:
\[
h = 16 \times 0.5736 \approx 9.2 \text{ ft}
\]
Thus, the ladder will reach approximately 9.2 feet high on the wall.
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