Question

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Find the missing part.

Answer 1

Answer:

$z=\frac{15\sqrt{3}}{2}$

Step-by-step explanation:

In leftmost triangle:

opposite side =y

adjacent=a

now, we can use trig formula

$tan(60)=\frac{y}{a}$

now, we can solve for y

$y=atan(60)$

In rightmost triangle:

adjacent=b

opposite=y

a+b=15

b=15-a

now, we can use trig formula

$tan(30)=\frac{y}{15-a}$

now, we can solve for y

$y=(15-a)tan(30)$

now, we can set them equal

and then we can solve for a

$atan(60)=(15-a)tan(30)$

$\sqrt{3}a\cdot \:3=\frac{\sqrt{3}\left(15-a\right)}{3}\cdot \:3$

$4\sqrt{3}a=15\sqrt{3}$

$a=\frac{15}{4}$

now, we can find b

$b=15-\frac{15}{4}$

$b=\frac{45}{4}$

now, we can use trig formula

$cos(30)=\frac{b}{z}$

now, we can find z

$z=\frac{\frac{45}{4}}{cos(30)}$

we can simplify it

and we get

$z=\frac{15\sqrt{3}}{2}$