Answer:
Therefore the distance across the patch of swamp water is 50 ft
Step-by-step explanation:
Given:
VW = 100 ft
WX = 60 ft
XZ = 30 ft
To Find:
ZY = l = ?
Solution:
In Δ VWX and Δ YZX
∠W ≅ ∠ Z …………..{measure of each angle is 90° given}
∠VXW ≅ ∠YXZ ..............{vertically opposite angles are equal}
Δ ABC ~ Δ DEC ….{Angle-Angle Similarity test}
If two triangles are similar then their sides are in proportion.
[tex]\frac{VW}{YZ} =\frac{WX}{ZX} =\frac{VX}{YX}\ \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]
On substituting the given values we get
[tex]\frac{100}{l} =\frac{60}{30}\\\\l=\frac{3000}{60}=50\ ft[/tex]
Therefore the distance across the patch of swamp water is 50 ft
