how high would i need to raise the end of a bed to get it to 30 degrees the total length of the bed is 86"

Answer 1

If you realize that this would make a 30-60-90 triangle the answer is really easy. The ratio of the sides of a 30-60-90 triangle are 1:2:sqrt(3) In your example, that means that the height off the ground would be half the length of the bed. Half of 86" is 43", so it will be 43" inches off the ground.

You can also use the sin(30) formula, but sin(30) is simply 0.5, so you get the same answer:

n = 86 sin(30)
n = 86 * 0.5
n = 43

So the answer either way is 43 inches off the ground.

Answer 2

The height divided by the length of a bed is by definition in any trig book the sin of 30 degrees.
The sin of 30 degrees is 1/2.

Therefore half of 86" is 43".

Your answer is 43 inches.

Answer 3

if the whole bed is 86" and you want an angle of elevation of 30 degrees then you want to raise the head or foot by 86sin30 inches...which comes to 43 inches

Answer 4

SOH-CAH-TOA, my friend, soh-cah-toa.
(Sine of an angle is Opposite over Hypotenuse on a triangle, Cosine is Adjacent over Hypotenuse, Tangent is Opposite over Adjacent)
- |\
x| \ 86"
- |_a\
a=30 deg.
so, sin(a)=x/86" and x=86sin(a)

Answer 5

30% of 86" , do your own homework from now on.

Answer 6

x/86" = sin(30)

sin(30) = 0.5

x is half of 86", so 43".

Answer 7

Will your teacher be coming by to "inspect" the bed later tonight?