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Math
GeometryElementary Geometry For College Students, 7e7th Edition

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Chapter 5.5, Problem 17E
BuyFindarrow_forward

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
BuyFindarrow_forward

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 m∠T=30°, m∠S=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 m∠T=30°, m∠S=60° and ST=12.

Since, the two angles, m∠T is 30° and m∠S 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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Sect-5.1 P-1ESect-5.1 P-2ESect-5.1 P-3ESect-5.1 P-4ESect-5.1 P-5ESect-5.1 P-6ESect-5.1 P-7ESect-5.1 P-8ESect-5.1 P-9ESect-5.1 P-10E
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