In the figure below, the distance from A to D is y, the distance from D to C is x, and the distance from C to B is A. Use the figure to solve the following problem. If A = 42°, BDC = 53°, AB = 13 and DB = 11, find x, then y. (Round each answer to one decimal place.) y = B D.
In the figure below, the distance from A to D is y, the distance from D to C is x, and the distance from C to B is A. Use the figure to solve the following problem. If A = 42°, BDC = 53°, AB = 13 and DB = 11, find x, then y. (Round each answer to one decimal place.) y = B D.
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 the figure below, the distance from \( A \) to \( D \) is \( y \), the distance from \( D \) to \( C \) is \( x \), and the distance from \( C \) to \( B \) is \( h \). Use the figure to solve the following problem.
If \( A = 42^\circ \), \( \angle BDC = 53^\circ \), \( AB = 13 \), and \( DB = 11 \), find \( x \), then \( y \). (Round each answer to one decimal place.)
\[
x = \underline{\ \ \ \ \ }
\]
\[
y = \underline{\ \ \ \ \ }
\]
**Diagram Explanation:**
The diagram is a triangle with points labeled \( A \), \( D \), \( B \), and \( C \). Point \( B \) is at the top, and the right angle is at \( C \). The line \( AD \) is labeled \( y \), the line \( DC \) is labeled \( x \), and the line \( CB \) is labeled \( h \).
The values given are:
- \( A \) is at an angle of \( 42^\circ \)
- \( \angle BDC \) is \( 53^\circ \)
- \( AB = 13 \)
- \( DB = 11 \)
**Objective:**
Calculate the unknown values \( x \) and \( y \) using the given measurements and trigonometric relationships.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe1933ef8-1f62-4aaa-99f9-8d3f9a87a376%2Fccb1cf1f-0b94-4a7b-9bb3-1896b98c43ee%2F4vyq36_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In the figure below, the distance from \( A \) to \( D \) is \( y \), the distance from \( D \) to \( C \) is \( x \), and the distance from \( C \) to \( B \) is \( h \). Use the figure to solve the following problem.
If \( A = 42^\circ \), \( \angle BDC = 53^\circ \), \( AB = 13 \), and \( DB = 11 \), find \( x \), then \( y \). (Round each answer to one decimal place.)
\[
x = \underline{\ \ \ \ \ }
\]
\[
y = \underline{\ \ \ \ \ }
\]
**Diagram Explanation:**
The diagram is a triangle with points labeled \( A \), \( D \), \( B \), and \( C \). Point \( B \) is at the top, and the right angle is at \( C \). The line \( AD \) is labeled \( y \), the line \( DC \) is labeled \( x \), and the line \( CB \) is labeled \( h \).
The values given are:
- \( A \) is at an angle of \( 42^\circ \)
- \( \angle BDC \) is \( 53^\circ \)
- \( AB = 13 \)
- \( DB = 11 \)
**Objective:**
Calculate the unknown values \( x \) and \( y \) using the given measurements and trigonometric relationships.
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