Question

Analyze the diagram below and complete the instructions that follow.

Find the value of x and the value of y.

Answer 1

Answer:

C. $x=2\sqrt{2}$, $y=2\sqrt{6}$    

Step-by-step explanation:

We have given a diagram of a right triangle. We are asked to find the value of x and y.

We can see that our triangle is 30,60,90 triangle.  

The smallest side is the side corresponding to 30 degree angle, that is x. The longer side is corresponding to 60 degree angle, that is y.

Since the measure of smallest side in a 30, 60, 90 triangle is half the measure of hypotenuse. Upon looking at our given triangle we can see that hypotenuse is $4\sqrt{2}$, therefore, measure of x will be,  

$x=\frac{4\sqrt{2}}{2}$

$x=2\sqrt{2}$

Now let us find the value of y (longer side) by multiplying the length of smaller side (x) by $\sqrt{3$, therefore, the measure of y will be,

$y=2\sqrt{2}*\sqrt{3}$

$y=2\sqrt{2*3}$

$y=2\sqrt{6}$

Upon looking at our given choices we can see that option C is the correct choice.

Answer 2

The value of $x$ is $\boxed{2\sqrt2 }$ and the value of y is $\boxed{2\sqrt 6 }.$Option (C) is correct.

Further explanation:

The Pythagorean formula can be expressed as,

$\boxed{{H^2} = {P^2} + {B^2}}.$

Here, H represents the hypotenuse, P represents the perpendicular and B represents the base.

The formula for sin of angle a can be expressed as

$\boxed{\sin a = \frac{P}{H}}$

Given:

The options are as follows,

(A). $x = 2\sqrt 2, y=8$

(B). $x = 2, y = 4\sqrt 6$

(C). $x = 2\sqrt 2, y = 2\sqrt 6$

(D). $x = 2\sqrt 3, y = 6\sqrt 3$

Explanation:

The value of $y$ can be obtained as follows,

$\begin{aligned}\sin {60^ \circ }&= \frac{y}{{4\sqrt 2 }}\\\frac{{\sqrt3 }}{2}&= \frac{y}{{4\sqrt 2 }}\\\frac{{\sqrt3 }}{2} \times 4\sqrt 2&= y\\2\sqrt6\\\end{aligned}$

The value of $x$ can be obtained as follows,

$\begin{aligned}\sin {30^ \circ }&= \frac{x}{{4\sqrt 2 }}\\\frac{1}{2}&= \frac{x}{{4\sqrt2 }}\\ \frac{{4\sqrt2 }}{2}&= x\\2\sqrt2&= x\\\end{aligned}$

The value of $x$ is $\boxed{2\sqrt2 }$ and the value of $y$ is $\boxed{2\sqrt 6 }$. Option (C) is correct.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function https://brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Trigonometry

Keywords: value of x, value of y, analyze, diagram, triangle, instructions, Pythagoras theorem.