   Chapter 5.5, Problem 17E 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

In Exercises 15 to 19, create drawings as needed. Given: ∆ R S T with m ∠ T - 30 ° ,   m ∠ S - 60 ° , and S T = 12 Find: R S and R T

To determine

To find:

RS and RT for a right RST with mT=30°, mS=60° and ST=12.

Explanation

Approach:

For a right triangle, for which the measure of the interior angles 30°, 60°, and 90°; if ‘a’ is the length of measure of the shorter leg; opposite to the angle 30°, then the length of the other two sides is given by

Length of the longer leg (opposite to 60°) =a3

Length of the hypotenuse (opposite to 90°) =2a.

In general

Length of the longer leg =3× (Length of the shorter leg)

Length of the hypotenuse =2× (Length of the shorter leg)

Calculation:

Given,

A right RST with mT=30°, mS=60° and ST=12.

Since, the two angles, mT is 30° and mS is 60°, the third triangle should be 90°.therefore, RST is a right triangle with right angle at R.

30°-60°-90° theorem.

In a right triangle whose angle measure 30°, 60°, and 90°, the hypotenuse has a length equal to twice the length of the shorter leg, and the longer leg is the product of 3 and the length of the shorter leg.

For the given triangle the hypotenuse given as ST=12.

Here, RT lies opposite to angle 60° of the triangle thus RT is the longer leg

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