Solve for æ in the following right triangle. 18 9/3 x =
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
![**Problem Statement:**
Solve for \( x \) in the following right triangle.
**Description of the Diagram:**
The image shows a right triangle with:
- Hypotenuse labeled as 18
- One leg labeled as \( x \)
- The other leg labeled as \( 9\sqrt{3} \)
The right angle is indicated between the legs of the triangle.
**Solution:**
Use the Pythagorean theorem, which states:
\[
a^2 + b^2 = c^2
\]
where \( c \) is the hypotenuse, and \( a \) and \( b \) are the other two sides.
Given:
- \( c = 18 \)
- One leg \( a = x \)
- The other leg \( b = 9\sqrt{3} \)
Substitute the values into the theorem:
\[
x^2 + (9\sqrt{3})^2 = 18^2
\]
Simplify:
\[
x^2 + 81 \times 3 = 324
\]
\[
x^2 + 243 = 324
\]
\[
x^2 = 324 - 243
\]
\[
x^2 = 81
\]
\[
x = \sqrt{81}
\]
\[
x = 9
\]
**Final Answer:**
\( x = 9 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42bd253a-231b-4c16-baac-6c405dc75416%2F04b98728-3b59-4565-930b-24ba4b2416e2%2Fcf9ktg_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Solve for \( x \) in the following right triangle.
**Description of the Diagram:**
The image shows a right triangle with:
- Hypotenuse labeled as 18
- One leg labeled as \( x \)
- The other leg labeled as \( 9\sqrt{3} \)
The right angle is indicated between the legs of the triangle.
**Solution:**
Use the Pythagorean theorem, which states:
\[
a^2 + b^2 = c^2
\]
where \( c \) is the hypotenuse, and \( a \) and \( b \) are the other two sides.
Given:
- \( c = 18 \)
- One leg \( a = x \)
- The other leg \( b = 9\sqrt{3} \)
Substitute the values into the theorem:
\[
x^2 + (9\sqrt{3})^2 = 18^2
\]
Simplify:
\[
x^2 + 81 \times 3 = 324
\]
\[
x^2 + 243 = 324
\]
\[
x^2 = 324 - 243
\]
\[
x^2 = 81
\]
\[
x = \sqrt{81}
\]
\[
x = 9
\]
**Final Answer:**
\( x = 9 \)
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