Mathematics: 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 hypotenuse 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

524.96 - 32.50 + x = 500492.46 + x = 500x = 500 - 492.46x = 7.54so she would need to deposit at least $ 7.54 to avoid a fee...

Triangle x y z is shown. angle x z y is a right angle.

Babyyygggirl26

09.01.2022

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

$cos(30\°)=\frac{\sqrt{3}}{2}$

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

$sin(30\°)=\frac{1}{2}$

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

$XZ=2\ units$

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

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

StartFraction StartRoot 3 EndRoot Over 3 EndFraction

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