How can you determine if a triangle is obtuse or acute given the three side lengths?
For example, given side lengths of "14, 21, and 25", how can you determine the type of triangle?
Thanks!
Got it -- In my original problem, you'd get $\displaystyle 14^2+21^2-25^2=12$, which is greater than 0 and therefore acute.
In my last post, I meant that if we look back at my original example, we can solve angle C to be approximately 88.8 degrees, and therefore the triangle would be acute? Is that another method to solve the problem?
Hi mathguy20 and Plato too,
Sides of triangle are a= 14 b= 21 c= 25 Angle A is opposite c
I calculate angle A is 88.8 degrees so the triangle is acute
another method
drop an altitude to a side Using Pytag write two equations in x for the alt segments and alt h. Solve for x and the other segment. Calculate angles using trig functions
bjh
Hello, mathguy20!
How can you determine if a triangle
is obtuse or acute given the three side lengths?
For example: given side lengths of 14, 21, and 25,
how can you determine the type of triangle?
Square the longest side; call this $\displaystyle \,x.$
Find the sum of the squares of the other two sides; call this $\displaystyle \,y.$
. . If $\displaystyle x > y$, obtuse triangle.
. . If $\displaystyle x < y$, acute triangle.
. . If $\displaystyle x = y$, right triangle.