SOLUTION: In an XYZ triangle, x=19.1m and y=32.7m and z=41.2m Suppose one angle is obtuse, which angle must it be? Determine the measure of the angle you identified in part a. Show your

Algebra ->  Triangles -> SOLUTION: In an XYZ triangle, x=19.1m and y=32.7m and z=41.2m Suppose one angle is obtuse, which angle must it be? Determine the measure of the angle you identified in part a. Show your       Log On


   

Question 1080313: In an XYZ triangle, x=19.1m and y=32.7m and z=41.2m
Suppose one angle is obtuse, which angle must it be?
Determine the measure of the angle you identified in part a. Show your work. Is the angle obtuse? Round to the nearest tenth.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2By%5E2-2xy%2Acos%28Z%29=z%5E2

-2xy%2Acos%28Z%29=z%5E2-x%5E2-y%5E2
cos%28Z%29=%28z%5E2-x%5E2-y%5E2%29%2F%28-2xy%29
cos%28Z%29=%28x%5E2%2By%5E2-z%5E2%29%2F%282xy%29
cos%28Z%29=%2819.1%5E2%2B32.7%5E2-41.2%5E2%29%2F%282%2A19.1%2A32.7%29
cos%28Z%29=-0.21081704

Measure of angle at point Z, 102.2 degrees

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

In an XYZ triangle, x=19.1m and y=32.7m and z=41.2m
Suppose one angle is obtuse, which angle must it be?
Determine the measure of the angle you identified in part a. Show your work. Is the angle obtuse? Round to the nearest tenth.
∡Z MUST be obtuse since it's opposite the longest side, z.

Use the law of cosines to find &#Z.