Question

Use similar triangles ABC and XYZ to find the missing height h. around to the nearest tenth if necessary.

Answer 1

Therefore,

The height is 23.3 ft.

Explanation:

Given:

ΔABC ~ ΔXYZ

AC = 108.5 ft

BC = h

XZ = 14 ft

YZ = 3ft

To Find:

h = ?

Solution:

Δ ABC ~ Δ XYZ….Given

If two triangles are similar then their sides are in proportion.

`(AB)/(XY) =(BC)/(YZ)=(AC)/(XZ) \textrm{corresponding sides of similar triangles are in proportion}\\`

Substituting the values we get

`(BC)/(YZ)=(AC)/(XZ)`

`(h)/(3)=(108.5)/(14)\\\\h=(325.5)/(14)=23.25=23.3`(nearest tenth)

Therefore,

The height is 23.3 ft.