In ΔBCD, the measure of ∠D=90°, DC = 55, CB = 73, and BD = 48. What ratio represents the cosine of ∠C?
In ΔBCD, the measure of ∠D=90°, DC = 55, CB = 73, and BD = 48. What ratio represents the cosine of ∠C?
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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Concept explainers
Ratios
A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.
Trigonometric Ratios
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
In ΔBCD, the measure of ∠D=90°, DC = 55, CB = 73, and BD = 48. What ratio represents the cosine of ∠C?
![**Mathematics Problem - Cosine Ratio in a Right Triangle**
**Problem Statement:**
In triangle \( \Delta BCD \), the measure of \( \angle D = 90^\circ \), \( DC = 55 \), \( CB = 73 \), and \( BD = 48 \). What ratio represents the cosine of \( \angle C \)?
---
In this problem, we are given a right triangle \( \Delta BCD \) with the right angle at \( D \). For a quick overview:
- \( \angle D = 90^\circ \)
- \( DC = 55 \)
- \( CB = 73 \)
- \( BD = 48 \)
To find the cosine of \( \angle C \), we will use the trigonometric ratio for cosine, which is defined as the adjacent side over the hypotenuse.
In right triangle \( \Delta BCD \):
- The side adjacent to \( \angle C \) is \( DC \).
- The hypotenuse of the triangle is \( CB \).
Thus,
\[ \cos(\angle C) = \frac{\text{Adjacent side}}{\text{Hypotenuse}} = \frac{DC}{CB} = \frac{55}{73} \]
So, the ratio that represents the cosine of \( \angle C \) is \( \frac{55}{73} \).
Note: The given condition states \( \angle D \) is a right angle, solidifying \( DC \) and \( BD \) as the two legs of the triangle with \( CB \) as the hypotenuse, simplifying our determination of trigonometric ratios.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0db0e8e9-7889-429c-9030-88511ed6e9f5%2Fee16ed8a-1efe-46f9-b868-a45ffb057d1c%2F8y2d20l_processed.png&w=3840&q=75)
Transcribed Image Text:**Mathematics Problem - Cosine Ratio in a Right Triangle**
**Problem Statement:**
In triangle \( \Delta BCD \), the measure of \( \angle D = 90^\circ \), \( DC = 55 \), \( CB = 73 \), and \( BD = 48 \). What ratio represents the cosine of \( \angle C \)?
---
In this problem, we are given a right triangle \( \Delta BCD \) with the right angle at \( D \). For a quick overview:
- \( \angle D = 90^\circ \)
- \( DC = 55 \)
- \( CB = 73 \)
- \( BD = 48 \)
To find the cosine of \( \angle C \), we will use the trigonometric ratio for cosine, which is defined as the adjacent side over the hypotenuse.
In right triangle \( \Delta BCD \):
- The side adjacent to \( \angle C \) is \( DC \).
- The hypotenuse of the triangle is \( CB \).
Thus,
\[ \cos(\angle C) = \frac{\text{Adjacent side}}{\text{Hypotenuse}} = \frac{DC}{CB} = \frac{55}{73} \]
So, the ratio that represents the cosine of \( \angle C \) is \( \frac{55}{73} \).
Note: The given condition states \( \angle D \) is a right angle, solidifying \( DC \) and \( BD \) as the two legs of the triangle with \( CB \) as the hypotenuse, simplifying our determination of trigonometric ratios.
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