6th Edition

ISBN: 9781285074672

Author: Larson

Publisher: CENGAGE L

Concept explainers

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made p…

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.

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Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 9.6, Problem 6E

To determine

Tofind:Length of legs of the triangle.

Expert Solution & Answer

Answer to Problem 6E

Longer leg is 53 inches and shorter leg is 5 inches

Explanation of Solution

Given information:

30∘−60∘−90∘ right angled triangle

Length of hypotenuse =10 inches

Concept Used:

In a 45∘−45∘−90∘ right angled triangle, length of both legs are equaland length of hypotenuse is given by product of length of any leg and square root of 2

In a 30∘−60∘−90∘ right angled triangle, length of longer leg is product of shorter length and square root of 3 and length of hypotenuse is given by twice the length of shorter leg.

Calculation:

Length of longer leg =x

Length of shorter leg =y

Length of hypotenuse in 30∘−60∘−90∘ twice the length of shorter leg.

Therefore-

2y=10⇒y=102⇒y=5 inches

Length of longer leg is product of shorter length and square root of 3

Therefore

x=y3⇒x=53 inches

Chapter 9.6, Problem 5E

Chapter 9.6, Problem 7E

Chapter 9 Solutions

ELEMENTARY+INTERMEDIATE ALGEBRA

Ch. 9.1 - Prob. 1C Ch. 9.1 - Prob. 2C Ch. 9.1 - Prob. 3C Ch. 9.1 - Prob. 4C Ch. 9.1 - Prob. 5C Ch. 9.1 - Prob. 6C Ch. 9.1 - Prob. 7C Ch. 9.1 - Prob. 8C Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E

Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E Ch. 9.1 - Prob. 9E Ch. 9.1 - Prob. 10E Ch. 9.1 - Prob. 11E Ch. 9.1 - Prob. 12E Ch. 9.1 - Prob. 13E Ch. 9.1 - Prob. 14E Ch. 9.1 - Prob. 15E Ch. 9.1 - Prob. 16E Ch. 9.1 - Prob. 17E Ch. 9.1 - Prob. 18E Ch. 9.1 - Prob. 19E Ch. 9.1 - Prob. 20E Ch. 9.1 - Prob. 21E Ch. 9.1 - Prob. 22E Ch. 9.1 - Prob. 23E Ch. 9.1 - Prob. 24E Ch. 9.1 - Prob. 25E Ch. 9.1 - Prob. 26E Ch. 9.1 - Prob. 27E Ch. 9.1 - Prob. 28E Ch. 9.1 - Prob. 29E Ch. 9.1 - Prob. 30E Ch. 9.1 - Prob. 31E Ch. 9.1 - Prob. 32E Ch. 9.1 - Prob. 33E Ch. 9.1 - Prob. 34E Ch. 9.1 - Prob. 35E Ch. 9.1 - Prob. 36E Ch. 9.1 - Prob. 37E Ch. 9.1 - Prob. 38E Ch. 9.1 - Prob. 39E Ch. 9.1 - Prob. 40E Ch. 9.1 - Prob. 41E Ch. 9.1 - Prob. 42E Ch. 9.1 - Prob. 43E Ch. 9.1 - Prob. 44E Ch. 9.1 - Prob. 45E Ch. 9.1 - Prob. 46E Ch. 9.1 - Prob. 47E Ch. 9.1 - Prob. 48E Ch. 9.1 - Prob. 49E Ch. 9.1 - Prob. 50E Ch. 9.1 - Prob. 51E Ch. 9.1 - Prob. 52E Ch. 9.1 - 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Tofind: Length of legs of the triangle .