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forsale [732]
3 years ago
8

Triangle X Y Z is shown. Angle X Z Y is a right angle. Angle Z X Y is 60 degrees and angle X Y Z is 30 degrees. The length of hy

potenuse X Y is 4. Given right triangle XYZ, what is the value of tan(Y)? One-half StartFraction StartRoot 3 EndRoot Over 3 EndFraction StartFraction StartRoot 3 EndRoot Over 2 EndFraction StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction

Mathematics
2 answers:
vladimir1956 [14]3 years ago
7 0

Answer:

StartFraction StartRoot 3 EndRoot Over 3 EndFraction

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

we know that

In the right triangle XYZ

cos(Y)=\frac{ZY}{XY} ---> adjacent side divided by the hypotenuse

substitute the values

cos(30\°)=\frac{ZY}{4}

Remember that

cos(30\°)=\frac{\sqrt{3}}{2}

so

substitute

\frac{\sqrt{3}}{2}=\frac{ZY}{4}

ZY=(4)\frac{\sqrt{3}}{2}

ZY=2\sqrt{3}\ units

step 2

sin(Y)=\frac{XZ}{XY} --> opposite side divided by the hypotenuse

substitute the values

sin(30\°)=\frac{XZ}{4}

Remember that

sin(30\°)=\frac{1}{2}

so

\frac{1}{2}=\frac{XZ}{4}

XZ=2\ units

step 3

tan(Y)=\frac{XZ}{ZY} --> opposite side divided by adjacent side

substitute the values

tan(Y)=\frac{2}{2\sqrt{3}}

tan(Y)=\frac{1}{\sqrt{3}}

Simplify

tan(Y)=\frac{\sqrt{3}}{3}

so

StartFraction StartRoot 3 EndRoot Over 3 EndFraction

Soloha48 [4]3 years ago
7 0

Answer:

b on edg

Step-by-step explanation:

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