### Trigonometry Problem: Right Triangle in a Unit Circle**Part 1:**The circle below is centered at the origin and has a radius of length 1 (so that the hypotenuse of the triangle shown has length 1). The measure of angle \( A \) is \( 30^\circ \).![Circle diagram labeled with a triangle showing angle A as 30 degrees. The hypotenuse is the radius, and a red side labeled OPP](part1-diagram.jpg)**Instructions:**Find the length of the red side of the triangle (labeled OPP), and use that to find the \( y \)-coordinate of the blue point. Enter exact expressions or round your answers to the nearest thousandth.- **Length of red side =** [Input Box]- **\( y \)-coordinate of blue point =** [Input Box]**Part 2:**The circle below is still centered at the origin and has a radius of length 1. The measure of angle \( B \) is \( 42^\circ \).![Circle diagram labeled with a triangle showing angle B as 42 degrees. The hypotenuse is the radius, and a red side labeled OPP](part2-diagram.jpg)**Instructions:**Again, find the length of the red side of the triangle (labeled OPP), and use that to find the \( y \)-coordinate of the blue point. Enter exact expressions or round your answers to the nearest thousandth.- **Length of red side =** [Input Box]- **\( y \)-coordinate of blue point =** [Input Box]**Explanation for the Diagrams:**Both diagrams consist of a circle centered at the origin (0,0) with a radius of 1 unit. Inside the circle, a right triangle is drawn such that the hypotenuse is the radius of the circle. - In the first diagram, the angle \( A \) at the origin is \( 30^\circ \).- In the second diagram, the angle \( B \) at the origin is \( 42^\circ \).The side labeled "OPP" (for opposite) is the length of the side opposite the given angle. The goal is to find this length and then use it to determine the \( y \)-coordinate of the point where the hypotenuse intersects the circle.

Answered: Image /qna-images/answer/6d036f48-ee61-488c-9e73-d0656a9e8170.jpg

origin and has a radius of length 1 (so that the hypotenuse of the triangle shown has length 1). The measure of angle A is 30°. OPP Find the length of the red side of the triangle (labeled OPP), and use that to find the y coordinate of the blue point. Enter exact expressions or round your answers to the nearest thousandth. Length of red side= y coordinate of blue point = Part 2: The circle below is still centered at the origin and has a radius of length 1. The measure of angle B is 42. Again, find the length of the red side of the triangle (labeled OFF) and use that to find the y coordinate of the blue point, Enter exact expressions or round your answers to the nearest thousandth Length of red side

origin and has a radius of length 1 (so that the hypotenuse of the triangle shown has length 1). The measure of angle A is 30°. OPP Find the length of the red side of the triangle (labeled OPP), and use that to find the y coordinate of the blue point. Enter exact expressions or round your answers to the nearest thousandth. Length of red side= y coordinate of blue point = Part 2: The circle below is still centered at the origin and has a radius of length 1. The measure of angle B is 42. Again, find the length of the red side of the triangle (labeled OFF) and use that to find the y coordinate of the blue point, Enter exact expressions or round your answers to the nearest thousandth Length of red side

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

### Trigonometry Problem: Right Triangle in a Unit Circle

**Part 1:**

The circle below is centered at the origin and has a radius of length 1 (so that the hypotenuse of the triangle shown has length 1). The measure of angle \( A \) is \( 30^\circ \).

![Circle diagram labeled with a triangle showing angle A as 30 degrees. The hypotenuse is the radius, and a red side labeled OPP](part1-diagram.jpg)

**Instructions:**

Find the length of the red side of the triangle (labeled OPP), and use that to find the \( y \)-coordinate of the blue point. Enter exact expressions or round your answers to the nearest thousandth.

- **Length of red side =** [Input Box]
- **\( y \)-coordinate of blue point =** [Input Box]

**Part 2:**

The circle below is still centered at the origin and has a radius of length 1. The measure of angle \( B \) is \( 42^\circ \).

![Circle diagram labeled with a triangle showing angle B as 42 degrees. The hypotenuse is the radius, and a red side labeled OPP](part2-diagram.jpg)

**Instructions:**

Again, find the length of the red side of the triangle (labeled OPP), and use that to find the \( y \)-coordinate of the blue point. Enter exact expressions or round your answers to the nearest thousandth.

- **Length of red side =** [Input Box]
- **\( y \)-coordinate of blue point =** [Input Box]

**Explanation for the Diagrams:**

Both diagrams consist of a circle centered at the origin (0,0) with a radius of 1 unit. Inside the circle, a right triangle is drawn such that the hypotenuse is the radius of the circle.
- In the first diagram, the angle \( A \) at the origin is \( 30^\circ \).
- In the second diagram, the angle \( B \) at the origin is \( 42^\circ \).

The side labeled "OPP" (for opposite) is the length of the side opposite the given angle. The goal is to find this length and then use it to determine the \( y \)-coordinate of the point where the hypotenuse intersects the circle.

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