Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![---
Find the measure of side c.
[Diagram Description]
The image shows a right-angled triangle ABC where ∠C is the right angle. The length of side \(a\) (adjacent to the right angle) is given as 30 meters. Angle ∠A is labeled as 32°. The side \(c\) represents the hypotenuse of the triangle and needs to be calculated.
---
c = __ m (Round the answer to the nearest whole number.)
---
In this problem, you are asked to find the length of the hypotenuse \(c\) of a right triangle given one of its angles and one of its side lengths. To solve this, you can use trigonometric ratios, specifically the cosine function, which relates the adjacent side and the hypotenuse in a right triangle.
The cosine of angle A is given by:
\[ \cos 32^\circ = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{a}{c} \]
Given:
\[ a = 30 \, \text{m} \]
Rearrange to solve for \(c\):
\[ c = \frac{a}{\cos 32^\circ} \]
After calculating, round the answer to the nearest whole number.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F959a643c-45ff-4cba-bf81-f285af0e5e62%2F41dd1a28-ce22-4133-b5ef-92e6ec8d78fb%2Fup5998_processed.png&w=3840&q=75)
Transcribed Image Text:---
Find the measure of side c.
[Diagram Description]
The image shows a right-angled triangle ABC where ∠C is the right angle. The length of side \(a\) (adjacent to the right angle) is given as 30 meters. Angle ∠A is labeled as 32°. The side \(c\) represents the hypotenuse of the triangle and needs to be calculated.
---
c = __ m (Round the answer to the nearest whole number.)
---
In this problem, you are asked to find the length of the hypotenuse \(c\) of a right triangle given one of its angles and one of its side lengths. To solve this, you can use trigonometric ratios, specifically the cosine function, which relates the adjacent side and the hypotenuse in a right triangle.
The cosine of angle A is given by:
\[ \cos 32^\circ = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{a}{c} \]
Given:
\[ a = 30 \, \text{m} \]
Rearrange to solve for \(c\):
\[ c = \frac{a}{\cos 32^\circ} \]
After calculating, round the answer to the nearest whole number.
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