Answer:
y=15/4
z=15/2
b=
[tex] \frac{15 \sqrt{3} }{4} [/tex]
Step-by-step explanation:
Use the equations:
[tex]y = h[/tex]
Where y is adjacent to angle 60 and 30
[tex]y = \frac{h}{2} [/tex]
Where y is adjacent to angles 60 and 90
[tex] \frac{h \sqrt{3} }{2} = y[/tex]
Where y is adjacent to angles 30 and 90
First lets find z
Segment a+b is the hypotenuse in the whole triangle.
Z is adjacent to angles 60 and 90, therefore we use the second formula.
Since we know the value of hypotenuse which is 15, subsitute h to 15 then simplify
[tex] \frac{15}{2} = z[/tex]
Next is y
y is a 60-90 segment like z, but this time we're going to use z as hypotenuse. Since y is a 60-90 segment, use second equation
[tex] \frac{ \frac{15}{2} }{2} = y[/tex]
[tex] \frac{15}{4} = y[/tex]
Lastly is b
b is a 30-90 segment therefore we will use the 3rd equation. We'll use z as hypotenuse as well.
[tex] \frac{ \frac{15}{2} \sqrt{3} }{2} = b[/tex]
[tex] \frac{15 \sqrt{3} }{4} = b[/tex]
