### Geometry Problem: Determining the Exact Value of x#### Problem Statement:Find the exact value of $x$ in the given figure.#### Diagram Explanation:- We have a right triangle with one angle marked as 45° and another angle marked as 60°.- One side adjacent to the 45° angle is labeled as "16".#### Answer Choices:A. $\frac{8 \sqrt{6}}{3}$B. $\frac{16 \sqrt{3}}{3}$C. $\frac{16 \sqrt{6}}{3}$D. $8 \sqrt{3}$### How to Solve:1. **Identify angles and relationships:** The triangle in question is a right triangle, and we know that with a 45° angle, it is also closely related to 45°-45°-90° and 30°-60°-90° triangles.2. **Use special right triangle properties:** - In a 45°-45°-90° triangle, the lengths of the legs are equal, and the hypotenuse is the leg length multiplied by $\sqrt{2}$. - In a 30°-60°-90° triangle, the sides are in the ratio 1 : $\sqrt{3}$ : 2.3. **Calculate based on side length information provided:** Utilize the properties of 30°-60°-90° triangle formulae or trigonometric identities to determine the unknown side $x$.### Solutions Explained:If we consider the given side (adjacent to the 45° and opposite to the 60°) and apply trigonometric properties (like sine, cosine relating the lengths of sides and the angles provided), we solve for $x$.After solving, we select from the answer choices:A. $\frac{8 \sqrt{6}}{3}$B. $\frac{16 \sqrt{3}}{3}$C. $\frac{16 \sqrt{6}}{3}$D. $8 \sqrt{3}$Keep in mind, the side ratios and the methodologies applied within such geometric constraints essentially guide to a derived choice showing correct mathematical approach.### Note:The exact method to reach the solution involves breaking and solving step-by-step angular approaches and confirming through selection which meets the

To Determine: Find the exact value of x

Answered: Find the exact value of x in the…

Math

Calculus

Find the exact value of x in the figure. O A. 8/6 16/3 OB. 3 600 16/6 Oc. 3 O D. 83 450 16

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

### Geometry Problem: Determining the Exact Value of x

#### Problem Statement:
Find the exact value of $x$ in the given figure.

#### Diagram Explanation:
- We have a right triangle with one angle marked as 45° and another angle marked as 60°.
- One side adjacent to the 45° angle is labeled as "16".

#### Answer Choices:
A. $\frac{8 \sqrt{6}}{3}$
B. $\frac{16 \sqrt{3}}{3}$
C. $\frac{16 \sqrt{6}}{3}$
D. $8 \sqrt{3}$

### How to Solve:

1. **Identify angles and relationships:**
The triangle in question is a right triangle, and we know that with a 45° angle, it is also closely related to 45°-45°-90° and 30°-60°-90° triangles.

2. **Use special right triangle properties:**
- In a 45°-45°-90° triangle, the lengths of the legs are equal, and the hypotenuse is the leg length multiplied by $\sqrt{2}$.
- In a 30°-60°-90° triangle, the sides are in the ratio 1 : $\sqrt{3}$ : 2.

3. **Calculate based on side length information provided:**
Utilize the properties of 30°-60°-90° triangle formulae or trigonometric identities to determine the unknown side $x$.

### Solutions Explained:

If we consider the given side (adjacent to the 45° and opposite to the 60°) and apply trigonometric properties (like sine, cosine relating the lengths of sides and the angles provided), we solve for $x$.

After solving, we select from the answer choices:
A. $\frac{8 \sqrt{6}}{3}$
B. $\frac{16 \sqrt{3}}{3}$
C. $\frac{16 \sqrt{6}}{3}$
D. $8 \sqrt{3}$

Keep in mind, the side ratios and the methodologies applied within such geometric constraints essentially guide to a derived choice showing correct mathematical approach.

### Note:
The exact method to reach the solution involves breaking and solving step-by-step angular approaches and confirming through selection which meets the

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