The question is looking for the amount of boxes (24 per box) needed for the event (300). If you multiply 24 by each number, you would be able to find the answer. 24*11 = 264, so that isn’t enough. 24*12 = 288, and that also isn’t enough. But if you do 24*13, you get 312, which gives you more than enough cupcakes for the event. So the answer is 13.
You have to build the triangles.
They are such that:
h is the common height
x is the horizontal distance from the plane to one stone
Beta is the angle between x and the hypotenuse
Then in this triangle: tan(beta) = h / x ......(1)
1 - x is the horizontal distance from the plane to the other stone
alfa is the angle between 1 - x and h
Then, in this triangle: tan (alfa) = h / [1 -x ] ...... (2)
from (1) , x = h / tan(beta)
Substitute this value in (2)
tan(alfa) = h / { [ 1 - h / tan(beta)] } =>
{ [ 1 - h / tan(beta) ] } tan(alfa) = h
[tan(beta) - h] tan(alfa) = h*tan(beta)
tan(beta)tan(alfa) - htan(alfa) = htan(beta)
h [tan(alfa) + tan(beta) ] = tan(beta) tan (alfa)
h = tan(beta)*tan(alfa) / (t an(alfa) + tan(beta) )
Answer:
16 feet, 18 feet, and 25 feet.
Step-by-step explanation:
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I've attached a photo of the solution below. Hope it helps!
