Answer:
Where's the cone at and I might be able to help
Step-by-step explanation:
Let h=height where top of ladder touches wall and x be distance from wall to bottom of ladder...
tana=h/x
a=arctan(h/x) and a≤75
arctan(h/x)≤75 now taking tan of both sides :P
h/x≤tan75 now we have an ugly x value that we need to get rid of:
Using the pythagorean theorem we know:
144=x^2+h^2, x^2=144-h^2, x=√(144-h^2) now we can use this in our inequality for x
h/√(144-h^2)≤tan75
h^2/(144-h^2)≤(tan75)^2
h^2≤144(tan75)^2-h^2(tan75)^2
h^2+h^2(tan75)^2≤144(tan75)^2
h^2(1+(tan75)^2)≤144(tan75)^2
h^2≤[144(tan75)^2]/(1+(tan75)^2)
h^2≤134.353829
h≤11.5911
So he cannot have the top of the ladder 11.8 ft above the ground and not exceed a 75° angle with the ground.
I worked it the hard way just to go through the process. However we could have used a simple trig function to see that maximum height of the top of the ladder....
sin75=h/12
h=12sin75
h≈11.59 ft. That would be the maximum height given that we did not want to exceed 75° with the ground.
<span>Exterior angle of a polygon = 72 degrees
Polygon has 5 sides.
Interior angle = 180 (n-2) / n
= 180 (5-2) / 5
= 108 degrees</span>
9514 1404 393
Answer:
8 ± √34 ≈ {2.169, 13.831}
Step-by-step explanation:
Let x represent one of the numbers. Then the other is 16 -x and their product is ...
x(16 -x) = 30
x^2 -16x = -30 . . . . . eliminate parentheses, multiply by -1
x^2 -16x +64 = 34 . . . . add 64 to complete the square
(x -8)^2 = 34 . . . . . . . . rewrite
x -8 = ±√34 . . . . . . . .square root
x = 8 ± √34 . . . . . . add 8
x ≈ {2.169, 13.831}
Minus 12 over 16 and 12 over 16
There you go!
