Select all the equations that can be used to identify the value of x in the triangle below:[Insert triangle image here]The given image shows a triangle that is divided into two right triangles. One right triangle has an angle of 30° and the other has an angle of 37°. The sides of the triangle are labeled as follows:- The side opposite the 30° angle is labeled as x.- The side adjacent to the 30° angle is labeled as h.- The hypotenuse of the right triangle with the 37° angle is labeled as 4.36.Here are the provided equations for selection:1. \(\cfrac{\sin(30°)}{4.36} = \cfrac{\sin(37°)}{x}\)2. \(\cfrac{\sin(37°)}{4.36} = \cfrac{\sin(30°)}{x}\)3. \(\cfrac{\cos(30°)}{4.36} = \cfrac{\cos(37°)}{x}\)4. \(\cfrac{4.36}{\sin(30°)} = \cfrac{x}{\sin(37°)}\)5. \(\cfrac{4.36}{\sin(37°)} = \cfrac{x}{\sin(30°)}\)6. \(\cfrac{\sin(30°)}{\sin(37°)} = \cfrac{x}{4.36}\)7. \(\cfrac{4.36}{h} = \cfrac{\sin(37°)}{\sin(30°)}\)8. \(\cfrac{\sin(30°)}{x} = 4.36 \cdot{\sin(37°)}\)### Explanation:Equations 1, 2, 4, 5, and 6 correctly use trigonometric ratios to set up proportions between the known values and the unknown value \(x\), making them valid options for solving for \(x\).Equations 3, 7, and 8 do not correctly set up the required trigonometric proportions to solve for \(x\) in this scenario. To solve for \(x\), you should use the trigonometric ratios for sine in the context of the given triangle.

Answered: Image /qna-images/answer/4aa78b88-44b0-4c61-876b-ab14dad4f94a.jpg

Select all the equations that can be used to identify the value of x in the triangle below: 0 0 30° sin(30°) 4.36 sin (37°) 4.36 cos (30°) 4.36 4.36 sin (30°) 4.36 sin(37°) X sin (30°) X cos (37°) sin (37°) X X = TRA h 4.36 37°

Select all the equations that can be used to identify the value of x in the triangle below: 0 0 30° sin(30°) 4.36 sin (37°) 4.36 cos (30°) 4.36 4.36 sin (30°) 4.36 sin(37°) X sin (30°) X cos (37°) sin (37°) X X = TRA h 4.36 37°

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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Question

Select all the equations that can be used to identify the value of x in the triangle below:

[Insert triangle image here]

The given image shows a triangle that is divided into two right triangles. One right triangle has an angle of 30° and the other has an angle of 37°. The sides of the triangle are labeled as follows:
- The side opposite the 30° angle is labeled as x.
- The side adjacent to the 30° angle is labeled as h.
- The hypotenuse of the right triangle with the 37° angle is labeled as 4.36.

Here are the provided equations for selection:

1. \(\cfrac{\sin(30°)}{4.36} = \cfrac{\sin(37°)}{x}\)
2. \(\cfrac{\sin(37°)}{4.36} = \cfrac{\sin(30°)}{x}\)
3. \(\cfrac{\cos(30°)}{4.36} = \cfrac{\cos(37°)}{x}\)
4. \(\cfrac{4.36}{\sin(30°)} = \cfrac{x}{\sin(37°)}\)
5. \(\cfrac{4.36}{\sin(37°)} = \cfrac{x}{\sin(30°)}\)
6. \(\cfrac{\sin(30°)}{\sin(37°)} = \cfrac{x}{4.36}\)
7. \(\cfrac{4.36}{h} = \cfrac{\sin(37°)}{\sin(30°)}\)
8. \(\cfrac{\sin(30°)}{x} = 4.36 \cdot{\sin(37°)}\)

### Explanation:

Equations 1, 2, 4, 5, and 6 correctly use trigonometric ratios to set up proportions between the known values and the unknown value \(x\), making them valid options for solving for \(x\).

Equations 3, 7, and 8 do not correctly set up the required trigonometric proportions to solve for \(x\) in this scenario.

To solve for \(x\), you should use the trigonometric ratios for sine in the context of the given triangle.

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