Question

PLEASE help! Math help? :)

In △XYZ , m∠X=38∘ , m∠Z=67∘ , and YZ=25 feet .

What is XZ ?

Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.

Answer 1

Answer: 39.2

Check out the attached image

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Step-by-step explanation:

Draw out the triangle or use the diagram provided by your teacher. It should look something similar to what I've attached.

Let m = length of side XZ

We are given that
angle Y = 75 degrees
angle Z = 67 degrees
which are the green angles shown in the diagram

Use the fact that the three angles (X,Y,Z) add to 180 degrees to find angle X
X+Y+Z = 180
X+75+67 = 180
X+142 = 180
X+142-142 = 180-142
X = 38

Now use the law of sines to find m
sin(X)/YZ = sin(Y)/XZ
sin(38)/25 = sin(75)/m
m*sin(38) = 25*sin(75)
m = 25*sin(75)/sin(38)
m = 39.22309 <<<--- make sure your calculator is in degree mode
m = 39.2

So XZ is roughly 39.2 feet in length