5) Consider the right triangle and find x: 18 51⁰ 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
![The question presents a right triangle problem that asks you to find the length of side \( x \).
The triangle includes:
- An angle of 51 degrees.
- A side opposite this angle, with a length of 18 units.
- A right angle.
- Side \( x \), which is adjacent to the 51-degree angle.
To solve for \( x \), we can use the tangent function in trigonometry, which relates the opposite side to the adjacent side in a right triangle:
\[
\tan(\text{angle}) = \frac{\text{opposite side}}{\text{adjacent side}}
\]
Here, \(\tan(51^\circ) = \frac{18}{x}\).
Rearrange this equation to solve for \( x \):
\[
x = \frac{18}{\tan(51^\circ)}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b06ad62-773d-462b-92f4-af8c7860e976%2F57481bcb-0fc2-4d79-ae33-e540f721fa38%2Fsrd5ca8_processed.png&w=3840&q=75)
Transcribed Image Text:The question presents a right triangle problem that asks you to find the length of side \( x \).
The triangle includes:
- An angle of 51 degrees.
- A side opposite this angle, with a length of 18 units.
- A right angle.
- Side \( x \), which is adjacent to the 51-degree angle.
To solve for \( x \), we can use the tangent function in trigonometry, which relates the opposite side to the adjacent side in a right triangle:
\[
\tan(\text{angle}) = \frac{\text{opposite side}}{\text{adjacent side}}
\]
Here, \(\tan(51^\circ) = \frac{18}{x}\).
Rearrange this equation to solve for \( x \):
\[
x = \frac{18}{\tan(51^\circ)}
\]
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