   Chapter 5.6, Problem 40E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Given: Δ R S T with right ∠ R S T ; m ∠ R = 30 ∘ and S T = 6 ; ∠ R S T is trisected by S M → and S N → Find: T N , N M , and M R

To determine

To find:

TN,NM,MR.

Explanation

Given:

In a ΔRST with right RST, mR=30,ST=6 and RST is trisected by SM,SN as shown below

Theorem used:

Angle bisector theorem:

If a ray bisects one angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the two sides that form the bisected angle.

Calculation:

Consider a ΔRST with right RST.

Since the RST is trisected, which is a right angle, we get mTSN=30,mNSM=30,mMSR=30.

Given that mR=30

mMSR=mR

Therefore triangle RMS is an isosceles triangle with MR=MS.

From the figure,

mTSM=mTSN+mNSM=30+30=60

mT=90mTRS=9030=60

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