Question

Find the missing side lengths. Leave your answers as radicals in simplest form.

Answer 1

Explanation:

For the question 1:

The given is a special right triangle with angle measures of

90-60-30 and side lengths represented by :

a - a
`√(3)` and 2a

The side length that sees 90 degrees is represented with a

The side length that sees 60 degrees is represented with a
`√(3)`

The side length that sees 30 degrees is represented with 2a

Here the side length that sees angle measure 60 is given as
`√(6)`

so a
`√(3)` =
`√(6)` to find the value of a we divide
`√(6)` with
`√(3)`

`(√(6) )/(√(3) )` =
`√(2)`

so y =
`√(2)` and x = 2
`√(2)`

for second question

the square value of hypotenuse is equal to sum of other two side length's square value

10^2 + 6^2 = x^2

100 + 36 = x^2

136 = x^2

`√(136)` = x