   Chapter 6.3, Problem 32E 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 ⊙ O (not shown), R S ¯ is a diameter and T is the midpoint of semicircle R T S ^ . What is the value of the ratio R T R S ? The ratio R T R O ?

To determine

To find:

To find value of the ratio RTRS and ratio RTRO.

Explanation

Given that, in O (not shown), RS¯ is a diameter and T is the midpoint of semicircle RTS^.

The diagrammatic representation is given below,

Given that RS¯ is diameter therefore, mRTS^=180°.

Then T is midpoint of RTS^. Therefore,

mRT^=mTS^=180°2=90°

That is mRT^=mTS^.

Therefore, RT=TS.

Also R and S on the circle to get the following,

mR=mTS^2=90°2=45°

mS=mRT^2=90°2=45°

Since inscribed angle are half of the arc length.

Since, RT=TS,OR=OS,andOT=OT.

By using SSS congruence to get the following,

ΔTORΔTOS

In congruent triangles corresponding parts are congruent (CPCTC). Therefore,

mTOR=mTOSmTOR=mTOS=90

A special type of right triangle is the 454590right triangle

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

In Exercises 13 and 14, find the inverse function of f. f(x)=4x+6

Calculus: An Applied Approach (MindTap Course List)

In Exercises 2340, find the indicated limit. 24. limx23

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Find the following products. (4+5i)(45i)

Trigonometry (MindTap Course List)

Sometimes, Always, or Never: If f(c) = 0, then c is a critical number.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 