Question

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

denominator rationalized.

Answer 1

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

`\sf x = 4√(6)` and
`\sf y = 6√(2)`

Explanation:

given:

• opposite length: y

• adjacent length: 2√6

• hypotenuse length: x

using tan rule:

`\sf tan(x)= (opposite)/(adjacent)`

`\sf tan(60)= (y)/(2√(6) )`

`\sf tan(60)*{2√(6)= y`

`\sf y = 6√(2)`

using cosine rule:

`\sf cos(x)= (adjacent)/(hypotensue)`

`\sf cos(60)= (2√(6) )/(x)`

`\sf x= (2√(6) )/(cos(60))`

`\sf x = 4√(6)`