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Alex73 [517]
3 years ago
11

Find the missing sides.

Mathematics
1 answer:
love history [14]3 years ago
6 0

Answer:

Part 3)

x=6\ units

y=3\ units

Part 4) x=18\sqrt{2}\ units

Step-by-step explanation:

Part 3)

<em>step 1</em>

Find the value of x

In the right triangle of the figure we know that

The cosine of angle of 30 degrees is equal to the adjacent side to angle of 30 degrees divide by the hypotenuse

so

cos(30\°)=\frac{3\sqrt{3}}{x}

and remember that

cos(30\°)=\frac{\sqrt{3}}{2}

substitute

\frac{\sqrt{3}}{2}=\frac{3\sqrt{3}}{x}

Simplify

x=(2*3)=6\ units

<em>step 2</em>

Find the value of y

In the right triangle of the figure we know that

The sine of angle of 30 degrees is equal to the opposite side to angle of 30 degrees divide by the hypotenuse

so

sin(30\°)=\frac{y}{x}

and remember that

sin(30\°)=\frac{1}{2}

substitute

\frac{1}{2}=\frac{y}{6}

y=6/2=3\ units

Part 4) Find the value of x

Applying the Pythagoras Theorem

x^{2} =18^{2} +18^{2} \\ \\x^{2} = 324+324\\ \\x^{2}=648\\ \\x=\sqrt{648}\ units

Simplify

x=18\sqrt{2}\ units

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