CK12 - Geometry

segment.

The TangentRatio

The first ratio to examinewhenstudyingright trianglesis the tangent.The tangentof an angleis the ratio
of the lengthof the oppositeside to the lengthof the adjacentside.The hypotenuseis not involvedin the
tangentat all. Be sure whenyou find a tangentthat you find the oppositeand adjacentsidesrelativeto the
anglein question.

For an acuteanglemeasuring , we define.

Example 2

Whatare the tangentsof and in the trianglebelow?

To find theseratios,first identifythe sidesoppositeand adjacentto eachangle.

So, the tangentof is about and the tangentof is.

It is commonto write insteadof. In this text we will use both notations.

ComplementaryAnglesin RightTriangles

Recallthat in all triangles,the sum of the measuresof all anglesmustbe. Sincea right anglehas a

measureof , the remainingtwo anglesin a right trianglemustbecomplementary. Complementary

angleshavea sum of. This meansthat if you knowthe measureof one of the smalleranglesin a right

triangle,you can easilyfind the measureof the other. Subtractthe knownanglefrom and you’llhave
the measureof the otherangle.

Example 3

Whatis the measureof

in the trianglebelow?