In ∆XYZ, XY=14, YZ=22, and XZ=28. What is the measure of angle Z to the nearest degree? * Law of Cosines
Cough cough 33
Oops just notice it said 28 the answer is wrong 👆 idk the answer for this one
so use the law of cosines, as directed.
Z is the angle between ZX and ZY, so
XY^2 = ZX^2 + ZY^2 - 2(ZX)(ZY) cosZ
33
To find the measure of angle Z in triangle XYZ using the Law of Cosines, we need to use the formula:
c^2 = a^2 + b^2 - 2ab * cos(C)
Where:
- c is the side opposite to angle C (in this case, side XZ)
- a and b are the other two sides (in this case, sides XY and YZ)
- C is the angle we want to find (angle Z)
Let's substitute the values we have into the formula:
28^2 = 14^2 + 22^2 - 2 * 14 * 22 * cos(Z)
Now we can solve this equation to find cos(Z).
784 = 196 + 484 - 616 * cos(Z)
784 = 680 - 616 * cos(Z)
616 * cos(Z) = 480
cos(Z) = 480 / 616
cos(Z) ≈ 0.7792
Now, to find the measure of angle Z, we need to take the inverse cosine (cos^-1) of 0.7792 using a calculator. This will give us the radian measure of Z.
cos^-1(0.7792) ≈ 0.6899 radians
To convert this into degrees, we multiply by 180/π:
0.6899 * (180/π) ≈ 39.563 degrees
Rounding to the nearest degree, the measure of angle Z in triangle XYZ is approximately 40 degrees.