CK12 - Trigonometry

Solution:The trianglesare similar

Recallthat for everyright triangle,we can use the PythagoreanTheoremto find the lengthof a missingside.

In ABCwe have:

(AC)^2 + 8^2 = 10^2

(AC)^2 + 64 = 100

(AC)^2 = 36

AC = 6

Similarly, in triangle DEFwe have:

= 5

2

(DF)

2

+ 4

2

(DF)^2 + 16 = 25

(DF)^2 = 9

DF = 3

Thereforethe sidesof the trianglesare proportional,with a ratio of 2:1.

Becausewe will alwaysbe able to use the PythagoreanTheoremin this way, two right triangleswill be
similarif the hypotenuseand one leg of one triangleare in proportionwith the hypotenuseand one leg of
the secondtriangle.This is the HL criteria.

Applicationsof similartriangles

Similartrianglescan be usedto solveproblemsin whichlengthsor distancesare proportional.The following
examplewill showyou how to solvesuchproblems.

Example6:Use similartrianglesto solvethe problem:

A tree castsa shadowthat is 24 feet long.A personwho is 5 feet tall is standingin front of the tree, and his
shadowis 8 feet long.Approximatelyhow tall is the tree?