Question

Find the measure of the missing sides in each special right triangle. Simplest radical form

Answer 1

X=
`8√(2)` Y=
`7√(2)`

Explanation:

The first one is 45-45-90 right angled isosceles triangle.

The length of the hypotenuse ie.X can be found with the help of Pythagoras Theorem.

`a^(2) + b^(2) = X^(2)`

where a and b are the remaining sides of the triangle,

`8^(2) +8^(2) =X^(2) \\2*8^(2) =X^(2)\\X=8√(2)`

X=
`8√(2)`

In the second triangle we have to apply trigonometry,

cos θ=
`(Length OfAdjacentSide)/(LengthOfHypotenuse)`

cos 30°=
`(√(3) )/(2)`

`(√(3) )/(2)`=
`(Y)/(14)`

Thus, Y=
`7√(2)` inches