Question

Someone help with process pleaseee

Answer 1

Answer: n= 6 x= 38.7427 f= 4.618802 h= 9.237604

Explanation:

for the first one:

there are 2 45 90 triangles. Since the sides of a 45 90 triangle are n for 45 and
`n√(2)` for the 90 degrees, that means that if
`6√(2) = n√(2)` then n is 6.

Second one:

You have to split the x into two parts.

Starting on the first part use the 30 60 90 triangle with given with the length for the 60°

60 =
`n√(3)`

so
`30=n√(3)`

n = 17.320506

so part of x is 17.320506

For the next triangle you would use Tan 35 =
`(15)/(y)`

this would equal 21.422201

adding both values up it would be 38.742707

Third question:

There is two 30 60 90 triangles

The 60° is equal to 8 which means
`8=n√(3)`

Simplifying this
`n=4.618802`

h = 2n. which is h= 9.237604

f=n f is 4.618802

Answer 2

Special right-angle triangle:

1) Ratio of angles: 45: 45: 90

Ratio of sides: 1: 1: √2

Sides are n, n, n√2

The side opposite to 90° = n√2

n√2 = 6√2

`\boxed{\sf n = 6}`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

2) Ratio of angles: 30: 60: 90

Ratio of side: 1: √3: 2

Sides are m, m√3, 2m.

Side opposite to 60° = m√3

m√3 = 30

`m = (30)/(√(3))\\\\\\m = (30√(3))/(3)\\\\m = 10√(3)`

Side opposite to 30° = m

m = 10√3

In ΔABC,

`Tan \ 35= (opposite \ side \ of \angle C )/(adjacent \ side \ of \angle C)\\\\\\~~~~~~0.7 = (15)/(CB)\\\\`

0.7 * CB = 15

`CB =(15)/(0.7)\\\\CB = 21.43`

x = m + CB

= 10√3 + 21.43

= 10*1.732 + 21.43

= 17.32 + 21.43

= 38.75

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

3) Ratio of angles: 30: 60: 90

Ratio of side: 1: √3: 2

Sides are y, y√3, 2y.

Side opposite to 60° = y√3

`\sf y√(3)= 8\\\\ ~~~~~ y = (8)/(√(3))\\\\~~~~~ y =(8*√(3))/(√(3)*√(3))\\\\\\~~~~~ y =(8√(3))/(3)`

Side opposite to 30° = y

`\sf f = y\\\\ \boxed{f = (8√(3))/(3)}`

Side opposite to 90° = 2y

h = 2y

`\sf h =2*(8√(3))/(3)\\\\\\\boxed{h=(16√(3))/(3)}`