Notes

Practice Problems

\({\textbf{1)}}\)\(\text{A triangle has sides with length }2,3, \text{ and } 4.\)

Is it a right, acute or obtuse triangle?

It is an obtuse triangle.

Show Work

\(\,\,\,\,\,\text{Check }a+b \gt c\)

\(\,\,\,\,\,2+3 \gt 4\)

\(\,\,\,\,\,a^2+b^2 \bigcirc c^2\)

\(\,\,\,\,\,(2)^2+(3)^2 \bigcirc (4)^2\)

\(\,\,\,\,\,4+9 \bigcirc 16\)

\(\,\,\,\,\,13 \lt 16\)

\(\,\,\,\,\,\text{It is an obtuse triangle.}\)

\({\textbf{2)}}\)\(\text{A triangle has sides with length }7,8, \text{ and } 9.\)

Is it a right, acute or obtuse triangle?

It is an acute triangle.

Show Work

\(\,\,\,\,\,\text{Check }a+b \gt c\)

\(\,\,\,\,\,7+8 \gt 9\)

\(\,\,\,\,\,a^2+b^2 \bigcirc c^2\)

\(\,\,\,\,\,(7)^2+(8)^2 \bigcirc (9)^2\)

\(\,\,\,\,\,49+64 \bigcirc 81\)

\(\,\,\,\,\,113 \gt 81\)

\(\,\,\,\,\,\text{It is an acute triangle.}\)

\({\textbf{3)}}\)\(\text{A triangle has sides with length }3,3, \text{ and } 5. \)

Is it a right, acute or obtuse triangle?

It is an obtuse triangle.

Show Work

\(\,\,\,\,\,\text{Check }a+b \gt c\)

\(\,\,\,\,\,3+3 \gt 5\)

\(\,\,\,\,\,a^2+b^2 \bigcirc c^2\)

\(\,\,\,\,\,(3)^2+(3)^2 \bigcirc (5)^2\)

\(\,\,\,\,\,9+9 \bigcirc 25\)

\(\,\,\,\,\,18 \lt 25\)

\(\,\,\,\,\,\text{It is an obtuse triangle.}\)

\({\textbf{4)}}\)\(\text{A triangle has sides with length }7,7, \text{ and } 1. \)

Is it a right, acute or obtuse triangle?

It is an acute triangle.

Show Work

\(\,\,\,\,\,\text{Check }a+b \gt c\)

\(\,\,\,\,\,1+7 \gt 7\)

\(\,\,\,\,\,a^2+b^2 \bigcirc c^2\)

\(\,\,\,\,\,(1)^2+(7)^2 \bigcirc (7)^2\)

\(\,\,\,\,\,1+49 \bigcirc 49\)

\(\,\,\,\,\,50 \gt 49\)

\(\,\,\,\,\,\text{It is an acute triangle.}\)

\({\textbf{5)}}\)\(\text{A triangle has sides with length }6,8, \text{ and } 10. \)

Is it a right, acute or obtuse triangle?

It is a right triangle.

Show Work

\(\,\,\,\,\,\text{Check }a+b \gt c\)

\(\,\,\,\,\,6+8 \gt 10\)

\(\,\,\,\,\,a^2+b^2 \bigcirc c^2\)

\(\,\,\,\,\,(6)^2+(8)^2 \bigcirc (10)^2\)

\(\,\,\,\,\,36+64 \bigcirc 100\)

\(\,\,\,\,\,100 = 100\)

\(\,\,\,\,\,\text{It is an right Triangle.}\)

\({\textbf{6)}}\)\(\text{A triangle has sides with length }1,1, \text{ and } \sqrt{2}.\)

Is it a right, acute or obtuse triangle?

It is a right triangle.

Show Work

\(\,\,\,\,\,\text{Check }a+b \gt c\)

\(\,\,\,\,\,1+1 \gt \sqrt{2}\)

\(\,\,\,\,\,a^2+b^2 \bigcirc c^2\)

\(\,\,\,\,\,(1)^2+(1)^2 \bigcirc \left(\sqrt{2}\right)^2\)

\(\,\,\,\,\,1+1 \bigcirc 2\)

\(\,\,\,\,\,2 = 2\)

\(\,\,\,\,\,\text{It is an right triangle.}\)

\({\textbf{7)}}\)\(\text{A triangle has sides with length }3,4, \text{ and } 8.\)

Is it a right, acute or obtuse triangle?

This is not a possible triangle.

Show Work

\(\,\,\,\,\,\text{Check }a+b \gt c\)

\(\,\,\,\,\,(3)+(4)\lt 8\)

\(\,\,\,\,\,\text{Due to triangle inequality theorem, it is not a possible triangle.}\)

See Related Pages\(\)

\(\bullet\text{ Pythagorean Theorem}\)
\(\,\,\,\,\,\,\,\,a^2+b^2=c^2\)…

\(\bullet\text{ Special Right Triangles (30-60-90 and 45-45-90)}\)
\(\,\,\,\,\,\,\,\,\) \(…\)

\(\bullet\text{ Triangle Inequality Theorem}\)
\(\,\,\,\,\,\,\,\,a+b\gt c,\, b+c \gt a , \, a+c \gt b\)…

About Andymath.com

Andymath.com is a free math website with the mission of helping students, teachers and tutors find helpful notes, useful sample problems with answers including step by step solutions, and other related materials to supplement classroom learning. If you have any requests for additional content, please contact Andy at tutoring@andymath.com. He will promptly add the content.

Topics cover Elementary Math, Middle School, Algebra, Geometry, Algebra 2/Pre-calculus/Trig, Calculus and Probability/Statistics. In the future, I hope to add Physics and Linear Algebra content.

Visit me on Youtube, Tiktok, Instagram and Facebook. Andymath content has a unique approach to presenting mathematics. The clear explanations, strong visuals mixed with dry humor regularly get millions of views. We are open to collaborations of all types, please contact Andy at tutoring@andymath.com for all enquiries. To offer financial support, visit my Patreon page. Let’s help students understand the math way of thinking!

Thank you for visiting. How exciting!