EmilyM02
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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 variables If your answer is not an integer leave it in simplest radical form Please help class=

Respuesta :

ShyzaSling

Answer:

option(D)

x= 30 , y = 10√3

Step-by-step 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

kudzordzifrancis

Answer:

[tex]x=30,y=10\sqrt{3}[/tex]

Step-by-step explanation:

Recall the mnemonics SOH CAH TOA.

We use the cosine ratio to find the value of [tex]x[/tex].

[tex]\cos(30\degree)=\frac{Adjacent}{Hypotenuse}[/tex]

This implies that;

[tex]\cos(30\degree)=\frac{x}{20\sqrt{3}}[/tex]

[tex]\frac{\sqrt{3}}{2} =\frac{x}{20\sqrt{3}}[/tex]

Cross multiply to get;

[tex]2x=20\sqrt{3}\times \sqrt{3}[/tex]

[tex]2x=60[/tex]

[tex]x=30[/tex]

Using the sine ratio

[tex]\sin(30\degree)=\frac{y}{20\sqrt{3} }[/tex]

[tex]\frac{1}{2}=\frac{y}{20\sqrt{3} }[/tex]

Tis implies that;

[tex]y=\frac{1}{2} \times 20\sqrt{3}[/tex]

[tex]y=10\sqrt{3}[/tex]

The correct choice is D.