Question

Could someone help solve for Y and X on the second triangle please? Thanks!

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

Diagram

x = ?

y = ?

z = ?

Step 02:

Similar Triangles

`(15)/(z)=(z)/(20)`

15 * 20 = z * z

300 = z ²

`z\text{ = }\sqrt[]{300}`

x ² + 15 ² = z ²

`\begin{gathered} x^2+225=(\sqrt[]{300})^2 \\ x^2=300\text{ - 225} \\ x\text{ = }\sqrt[]{75} \end{gathered}`

y² + z² = 20²

`\begin{gathered} y^2+(\sqrt[]{300})^2=400 \\ y^2=400-300 \\ y=\sqrt[]{100}\text{ = 10} \end{gathered}`

The answer is:

x = √75 = 5√3

y = 10

z = √300 = 10√3