+709 Ok so I'm stuck on these 4 geometry problems. I can't ask my teacher for help and the internet has been useless so far.
Tell if these measures can be the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. Explain how you know.
1. (9,12, and 16) 2. (11,14, and 27) 3. (1.5,3.6, and 3.9) 4. (2,3.7, and 4.1)
+129849 1. [9, 12, 16] the triangle is possible
The triangle 9-12-15 is a right triangle with the angle opposite the longest side = 90°
Therefore.......the angle opposite the longest side here will be > 90° since 16 >15
Then, this trangle is obtuse [we can prove this using the Law of Cosines]
2. (11,14, and 27) this triangle is not possible
Remember that the sum of any two sides of a triangle must be greater than the remaining sde.....but.... 11 + 14 = 25 and 25 < 27 ....so......no triangle is formed
3. (1.5,3.6, and 3.9)
Remember that, if we multiply every side by 10, we will have a similar triangle to the one given....so.....this triangle will be 15 - 36 - 39
Note 15^2 + 36^2 = 39^2 ....so this triangle is a right triangle
4. (2,3.7, and 4.1) multiply by 10 again and we have 20 - 37 - 41
Note that sqrt[20^ + 37^2] = about 42.05
So.....since a right triangle is formed with sides of 20, 37 and ≈ 42.05
And the angle opposite the right triangle with a side of about 42.05 would be 90°
But this triangle has a third side which is < 42.05
Thus.....the angle opposite the side 41 in a 20 - 37 - 41 triangle will be < 90°
So.....this triangle is acute because the other two angles will also be acute [we can prove this using the Law of Sines]
