Question

What is the measure of y?327LYZNХy = [?]Give your answer in simplest form.I

Answer 1

Given:

The length of the triangle is: 27, 3, x, y, and z.

Find: Value of "y"

Sol:

In triangle ACD is:

Use Pythagoras theorem:

`\text{ Hypotenuse}^2=\text{ Base}^2+\text{ Perpendicular}^2`

Apply for triangle ACD then:

`\begin{gathered} AC^2=AD^2+CD^2 \\ \\ (27+3)^2=z^2+x^2 \\ \\ 30^2=z^2+x^2...........(1) \end{gathered}`

In triangle CBD

Apply theorem then:

`x^2=27^2+y^2.........(2)`

In Triangle ABD

Apply theorem then:

`\begin{gathered} z^2=3^2+y^2...........(3) \\ \end{gathered}`

From eq (2) and eq(3) put the value in eq(1) then:

`\begin{gathered} 30^2=z^2+x^2 \\ \\ 30^2=3^2+y^2+27^2+y^2 \\ \\ 900=9+2y^2+729 \\ \\ 900-(729+9)=2y^2 \\ \\ 162=2y^2 \\ \\ y^2=(162)/(2) \\ \\ y^2=81 \\ \\ y=9 \end{gathered}`

So the value of "y" is 9.