i app.edulastic. Dulce's Folder Bell Schedules - A... Biology KAREN 4TH HBUHSD E- Question 35/36 NEXT BOOKM. Bookmar 35 Solve for x. 60° 3V3 A 9 B 9v2 C 6V3 D 9V3
i app.edulastic. Dulce's Folder Bell Schedules - A... Biology KAREN 4TH HBUHSD E- Question 35/36 NEXT BOOKM. Bookmar 35 Solve for x. 60° 3V3 A 9 B 9v2 C 6V3 D 9V3
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter1: The Six Trigonometric Functions
Section1.2: The Rectangular Coordinate System
Problem 92PS: Draw an angle in standard position whose terminal side contains the point (2, –3). Find the...
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35. Solve for x.
![### Trigonometry Problem: Solve for x
In this problem, we are given a right triangle with the following parameters:
- One angle is 60°
- The length of the side opposite the 60° angle is \(3\sqrt{3}\)
- We need to solve for the length of the hypotenuse \(x\)
#### Given:
- Angle \( \theta = 60° \)
- Opposite side to angle \( \theta \): \( 3\sqrt{3} \)
- Right angle
#### Options:
A. \( 9 \)
B. \( 9\sqrt{2} \)
C. \( 6\sqrt{3} \)
D. \( 9\sqrt{3} \)
#### Solution:
To solve for \( x \), we can use the relationship between the sides of a 30°-60°-90° triangle. In a 30°-60°-90° triangle:
- The length of the hypotenuse is twice the length of the shorter leg (opposite the 30° angle).
- The length of the longer leg (opposite the 60° angle) is \( \sqrt{3} \) times the length of the shorter leg.
Given that the length of the longer leg is \( 3\sqrt{3} \):
- Let the shorter leg be \( y \).
- Therefore, \( y \cdot \sqrt{3} = 3\sqrt{3} \)
- Solving for \( y \): \( y = 3 \)
- The hypotenuse \( x \) is twice the length of the shorter leg:
- \( x = 2 \cdot y \)
- Thus, \( x = 2 \cdot 3 = 6 \)
#### Correct Answer:
C. \( 6\sqrt{3} \)
However, since none of the options directly align with this solution, it might be necessary for a reevaluation, or there may have been a different approach expected in the configuration of this problem that needs a more detailed insight.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F92094b20-9792-4363-b2eb-d85ac30bc889%2F5e2161b8-a3e9-46dd-b471-6c4ece427f11%2Furg5uco_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Trigonometry Problem: Solve for x
In this problem, we are given a right triangle with the following parameters:
- One angle is 60°
- The length of the side opposite the 60° angle is \(3\sqrt{3}\)
- We need to solve for the length of the hypotenuse \(x\)
#### Given:
- Angle \( \theta = 60° \)
- Opposite side to angle \( \theta \): \( 3\sqrt{3} \)
- Right angle
#### Options:
A. \( 9 \)
B. \( 9\sqrt{2} \)
C. \( 6\sqrt{3} \)
D. \( 9\sqrt{3} \)
#### Solution:
To solve for \( x \), we can use the relationship between the sides of a 30°-60°-90° triangle. In a 30°-60°-90° triangle:
- The length of the hypotenuse is twice the length of the shorter leg (opposite the 30° angle).
- The length of the longer leg (opposite the 60° angle) is \( \sqrt{3} \) times the length of the shorter leg.
Given that the length of the longer leg is \( 3\sqrt{3} \):
- Let the shorter leg be \( y \).
- Therefore, \( y \cdot \sqrt{3} = 3\sqrt{3} \)
- Solving for \( y \): \( y = 3 \)
- The hypotenuse \( x \) is twice the length of the shorter leg:
- \( x = 2 \cdot y \)
- Thus, \( x = 2 \cdot 3 = 6 \)
#### Correct Answer:
C. \( 6\sqrt{3} \)
However, since none of the options directly align with this solution, it might be necessary for a reevaluation, or there may have been a different approach expected in the configuration of this problem that needs a more detailed insight.
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