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
Accepted Solution
A:
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 :)