Question

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

Answer 1

Answer:

Therefore,

The height is 23.3 ft.

Step-by-step 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.  

$\dfrac{AB}{XY} =\dfrac{BC}{YZ}=\dfrac{AC}{XZ} \textrm{corresponding sides of similar triangles are in proportion}$  

Substituting the values we get

$\dfrac{BC}{YZ}=\dfrac{AC}{XZ}$

$\dfrac{h}{3}=\dfrac{108.5}{14}\\\\h=\dfrac{325.5}{14}=23.25=23.3$(nearest tenth)

Therefore,

The height is 23.3 ft.