Question

I need the incomplete fraction answer for:
y=
z=
b=
Thx

Answer 1

y=15/4

z=15/2

b=

`(15 √(3) )/(4)`

Explanation:

Use the equations:

`y = h`

Where y is adjacent to angle 60 and 30

`y = (h)/(2)`

Where y is adjacent to angles 60 and 90

`(h √(3) )/(2) = y`

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

`(15)/(2) = z`

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

`( (15)/(2) )/(2) = y`

`(15)/(4) = y`

Lastly is b

b is a 30-90 segment therefore we will use the 3rd equation. We'll use z as hypotenuse as well.

`( (15)/(2) √(3) )/(2) = b`

`(15 √(3) )/(4) = b`

Answer 2

Y = 15sqrt(3)/4

Z = 15sqrt(3)/2

b = 45/4

Explanation:

Sin(60) =Z/15

sqrt(3)/2 = Z/15

Z = 15sqrt(3)/2

Sin(30) = Y/Z

½ = Y/Z

Y = ½(15sqrt(3))/2 = 15sqrt(3)/4

Cos(30) = b/Z

sqrt(3)/2 = b/Z

b = 15sqrt(3)/2 × sqrt(3)/2

b = 45/4

sqrt is square root/radical