Describe three ways to determine the measure of segment YZ. Triangle X Y Z is shown. Angle X Y Z is a right angle and angle Z X Y is 30 degrees. The length of hypotenuse X Z is 50 meters.

Using 3 different methods, we can find that YZ = 25m

For a given triangle rectangle with a known angle θ and a hypotenuse H, we can write the trigonometric relations

sin(θ) = (opposite cathetus)/H

cos(θ) = (adjacent cathetus)/H

tan(θ) = (opposite cathetus)/(adjacent cathetus)

Now, in the given image we can see that:

θ = 30°

H = 50m

XY = adjacent cathetus

YZ = opposite cathetus.

We want to find YZ, so with the known things, we can use the first relation:

Now let's try another way.

We know that the sum of the internal angles of a triangle is always equal to 180°

In a triangle rectangle, we always have an angle equal to 90°.

Then the missing angle for our triangle can be computed from:

Z + 90° + 30° = 180°

Z = 180° - 90° - 30° = 60°

From this angle, the side YZ is the adjacent cathetus, then we can use the second trigonometric relation:

Third way.

Whit the same angle we could find the side XY, the opposite cathetus, with:

Now that we know one of the catheti, we can use the last trigonometric relation

If you want to learn more about triangle rectangles, you can read:

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step-by-step explanation: