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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.

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 Hypo class=

Sagot :

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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:

[tex]sin(30\°) = YZ/50m[/tex]

[tex]sin(30\°)*50m = YZ = 25m[/tex]

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:

[tex]cos(60\°) = YZ/50m\\cos(60\°)*50m = YZ = 25m\\[/tex]

Third way.

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

[tex]sin(60\°) = XY/50m \\sin(60\°)*50m = XY = 43.3m[/tex]

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

[tex]tan(60\°) = XY/YZ = 43.3m/YZ \\YZ = 43.3m/tan(60\°) = 25m\\[/tex]

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

https://brainly.com/question/24330420

hobomakayla

Answer:

Solve the equation where the sine of 30 degrees is equal to YZ/50.

Solve 180 – (30 + 90) = 60 to find the measure of angle Z. Then use the cosine of Z to write and solve an equation.

Use the 30°-60°-90° triangle theorem to find that YZ = 50/2.

Step-by-step explanation:

edge 2022

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