Question

analyze the diagram below and complete the instructions that follow. find the value of x and the value of y

Answer 1

Answers:
x = 2√2 units
y = 2√6 units

Explanation:
The given diagram is a right-angled triangle. This means that the special trig functions can be applied.
These functions are as follows:
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent

For getting x and y, we can choose to either work with θ = 30 or θ = 60.
I will work with 30.

1- For x:
We have:
θ = 30
x is the opposite side to θ
4√2 is the hypotenuse
Therefore, we can apply the sine function as follows:
sin θ = opposite / hypotenuse
sin (30) = x / 4√2
x = sin (30) * 4√2
x = 2√2 units

2- For y:
We have:
θ = 30
x is the adjacent side to θ
4√2 is the hypotenuse
Therefore, we can apply the cosine function as follows:
cos θ = adjacent / hypotenuse
cos (30) = y / 4√2
y = cos (30) * 4√2
y = 2√6 units

Hope this helps :)

Answer 2

The value of $x$ is $\boxed{2\sqrt2 }$ and the value of $y$ is $\boxed{2\sqrt 6 }.$

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

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

The formula for cos of angle a can be expressed as

$\boxed{\cos a=\frac{B}{H}}$

The formula for tan of angle a can be expressed as

$\boxed{\tan a= \frac{P}{B}}$

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 $\boxed{2\sqrt 6 }.$

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 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.