Triangle Inequality, sides, angle relationships

Sum of angles of triangle =

180

possible

A builder has decided to use triangles within his design. He decided to use dimensions of 15 ft, 13 ft and 14 ft. Are these possible or impossible dimensions?

In ∆ABC, AB=10, BC=9, CA=11 largest angle of triangle is

Angle B

33< x < 43

In a triangle with two sides of lengths 5 and 38, what are the possible lengths of the third side?

Between 22 and 38

In a triangle with two sides of lengths 8 and 30, what are the possible lengths of the third side?

Bigger than 3 and smaller than 15.

In a triangle with two sides of lengths 9 and 6, what are the possible lengths of the third side?

In ∆DEF, m∠D=64, m∠E=60, m∠F=56 which is shortest side of triangle

Side DE

In ∆DEF, m∠D=60, m∠E=70, m∠F=50 which is shortest side of triangle

Side DF

impossible

The blueprints for a bridge label the triangles within the design as having side lengths of 20 ft, 20 ft and 40 ft. Are these possible or impossible side lengths?

Triangle Inequality Theorem (∆ Inequality Thm)

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

In ∆BCD, m∠B=62, m∠D=60, m∠C=58 the longest side of the ∆is

side DC

Longest side of triangle is opposite

the largest angle

Shortest side is opposite

the smaller angle