Question

Given the following triangle side lengths, identify the triangle as acute, right or obtuse. Show your work. a. 5 in, 6 in, 7 in b. 18 in, 9 in, 12 in

Answer 1

These are the formulas that will help you determine which type of triangle they are:

a^2+b^2 < c^2      ----> Obtuse Triangle

a^2+b^2 > c^2      ----> Actue Triangle

a^2+b^2 = c^2      ----> Right Triangle

Okay so now that you know that information, lets get into it :)

a. 5 in, 6 in, 7 in

You're going to take the smallest numbers, 5 and 6, and add them, if it equals a larger number than 7 then its a triangle and you have to determine if its an obtuse, right or acute triangle. In this case it is a triangle because 5 + 6 = 11 aka larger than 7.

The way you'll set this up is:

5^2 + 6^2 = 7^2

solve
25+36=49      ----->     25+36=61

61 > 49 or a^2 + b^2 > c^2

61 > is greater than 49

If you look ate the formulas that are above, this is an acute triangle.

b. 18 in, 9 in, 12 in

In this question, 9 and 12 are the smallest numbers that equal 21 and 21 is larger than 18 so, this is a triangle.

9^2 + 12^2 = 18^2

Solve
81 + 144 = 324      ---->      81 + 144 = 225

225 < 324 or a^2+b^2 < c^2

225 < is less than 324

If you look ate the formulas that are above, this is an obtuse triangle.

Something to just remember:

Sometimes you'll get a question which is like,
4 in, 5 in, 10 in
In this situation, if you add the smallest numbers which are, 4 and 5, you get 9, which is less than the larger number you have, 10. That means it is not a triangle. Just something to be aware about :)

I hope this helped you!