Question

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!!

Answer 1

`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.

Answer 2

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