176k views
4 votes
For the following question, find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form. Please help!!

For the following question, find the value of the variable(s). If your answer is not-example-1
User Matos
by
6.7k points

2 Answers

3 votes

Answer:


x=30,y=10√(3)

Explanation:

Recall the mnemonics SOH CAH TOA.

We use the cosine ratio to find the value of
x.


\cos(30\degree)=(Adjacent)/(Hypotenuse)

This implies that;


\cos(30\degree)=(x)/(20√(3))


(√(3))/(2) =(x)/(20√(3))

Cross multiply to get;


2x=20√(3)* √(3)


2x=60


x=30

Using the sine ratio


\sin(30\degree)=(y)/(20√(3) )


(1)/(2)=(y)/(20√(3) )

Tis implies that;


y=(1)/(2) * 20√(3)


y=10√(3)

The correct choice is D.

User Pajamas
by
6.3k points
1 vote

Answer:

option(D)

x= 30 , y = 10√3

Explanation:

Given in the question, a right angle triangle whose

hypotenuse = 20√3

We will use pythagorus theorem and trigonometry identities to find the value of x and y

Formula to use

sinФ = base / hypotenuse

sin(30) = y / 20√3

y = sin(30) x 20√3

y = 10√3

hypotenuse² = base² + height²

(20√3)² = (10√3)² + x²

(20√3)² - (10√3)² = x²

x² = 900

x = √900

x = 30

so, the value of x = 30 and y = 10√3

User RavuAlHemio
by
6.3k points