Question

Find the missing side lengths. Answers are in simplest radical form with the
denominator rationalized.

Answer 1

Step-by-step explanation:

Given is the 30°x60°x90° right triangle.

The ratio of its sides is:

• 1 : √3 : 2

Find the missing sides using the ratio above:

• x = 2*2√6 = 4√6
• y = 2√6*√3 = 2*3√2 = 6√2

Answer 2

Answer:

$\sf x = 4\sqrt{6}$   and   $\sf y = 6\sqrt{2}$

step-by-step explanation:

given:

• opposite length: y

• adjacent length: 2√6

• hypotenuse length: x

using tan rule:

$\sf tan(x)= \dfrac{opposite}{adjacent}$

$\sf tan(60)= \dfrac{y}{2\sqrt{6} }$

$\sf tan(60)*{2\sqrt{6}= y$

$\sf y = 6\sqrt{2}$

using cosine rule:

$\sf cos(x)= \dfrac{adjacent}{hypotensue}$

$\sf cos(60)= \dfrac{2\sqrt{6} }{x}$

$\sf x= \dfrac{2\sqrt{6} }{cos(60)}$

$\sf x = 4\sqrt{6}$