   Chapter 6.1, Problem 10E 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: S T = 1 2 ( S R )  in  ⊙ Q   S R ¯  is a diameter Find: a) m S T ⌢ b) m T R ⌢ c) m S T R ⌢ d) m ∠ S (HINT: Dra Q T ¯ . )

To determine

a)

To calculate:

The mST from the provided figure.

Explanation

Given:

In a circle Q, ST=12(SR) where SR¯ is the diameter.

Theorem used:

The measure of an inscribed angle of a circle is one-half the measure of its intercepted arc.

An angle inscribed in a semicircle is a right angle.

Calculation:

From the figure we see that STR is a semicircle. Join TR¯ as shown below

We know that the angle inscribed in a semicircle is a right angle. Therefore STR=90.

Given that ST=12(SR).

In a right triangle STR, the hypotenuse is twice as longer than the shorter leg.

Hence the angles in right triangle STR are 30,60,90

To determine

b)

To calculate:

The mTR from the provided figure.

To determine

c)

To calculate:

The mSTR from the provided figure.

To determine

d)

To calculate:

The mS from the provided figure.

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