Question

In the figure below, find the exact value of z. (do not approximate answer.)

Answer 1

z =
`√(10)`

Explanation:

Small triangle:

short leg = 2

long leg = z

Large triangle

short leg = z

long leg = 5

-------------------------

The triangles are similar therefor

Sshort / Lshort = Slong / Llong

2/z = z/5

multiply both sides by z

2 =
`z^(2)`/5

multiply both sides by 5

10 =
`z^(2)`

Take the square root of both sides

z =
`√(10)`