Find a. a ft a= Question Help: Message instructor Submit Question a 5.4 ft 300
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°.
Related questions
Question
![### Finding the Length of Side 'a' in a Right Triangle
In this exercise, you are asked to determine the length of side \(a\) in a right triangle.
**Diagram Explanation:**
- The given right triangle has one angle measuring \(30^\circ\).
- The hypotenuse (the side opposite the right angle) is given as 5.4 feet.
- You are asked to find the length of side \(a\), which is opposite the \(30^\circ\) angle.
**Mathematical Context:**
In a right triangle, you can use trigonometric ratios to find missing sides. Since you know the length of the hypotenuse and the measure of one of the non-right angles, you can use the sine function:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
Here, \(\theta = 30^\circ\), the hypotenuse is 5.4 feet, and the side opposite \(\theta\) is \(a\).
Therefore,
\[ \sin(30^\circ) = \frac{a}{5.4 \text{ ft}} \]
Since
\[ \sin(30^\circ) = 0.5 \]
We have:
\[ 0.5 = \frac{a}{5.4} \]
\[ a = 0.5 \times 5.4 \]
\[ a = 2.7 \text{ ft} \]
**Question:**
Find \(a\).
\[ a = \]
\(\boxed{\text{ ft}}\)
**Additional Support:**
If you need help, you can:
- Click on "Message instructor."
Once you have your answer, press the "Submit Question" button to check your solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdc1123ec-a0e0-4e35-afe0-df78f47a58b5%2F171a33a5-7427-478f-9a5c-724898a5b4ff%2Fxc36jc9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Finding the Length of Side 'a' in a Right Triangle
In this exercise, you are asked to determine the length of side \(a\) in a right triangle.
**Diagram Explanation:**
- The given right triangle has one angle measuring \(30^\circ\).
- The hypotenuse (the side opposite the right angle) is given as 5.4 feet.
- You are asked to find the length of side \(a\), which is opposite the \(30^\circ\) angle.
**Mathematical Context:**
In a right triangle, you can use trigonometric ratios to find missing sides. Since you know the length of the hypotenuse and the measure of one of the non-right angles, you can use the sine function:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
Here, \(\theta = 30^\circ\), the hypotenuse is 5.4 feet, and the side opposite \(\theta\) is \(a\).
Therefore,
\[ \sin(30^\circ) = \frac{a}{5.4 \text{ ft}} \]
Since
\[ \sin(30^\circ) = 0.5 \]
We have:
\[ 0.5 = \frac{a}{5.4} \]
\[ a = 0.5 \times 5.4 \]
\[ a = 2.7 \text{ ft} \]
**Question:**
Find \(a\).
\[ a = \]
\(\boxed{\text{ ft}}\)
**Additional Support:**
If you need help, you can:
- Click on "Message instructor."
Once you have your answer, press the "Submit Question" button to check your solution.
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