Answer:
Step-by-step explanation:
here is some helpful trig function reminders.. copy this and keep it
Use SOH CAH TOA to recall how the trig functions fit on a triangle
SOH: Sin(Ф)= Opp / Hyp
CAH: Cos(Ф)= Adj / Hyp
TOA: Tan(Ф) = Opp / Adj
they ask how long is the ladder
they give us the opposite side (8) and the adjacent side (6)
and the Hyp is the length of the ladder. They expect you to sort this out in your head. :/
there is two steps .. we'll solve for the angle.. then we can use that to find the Hyp side..(long side of triangle) which is the ladder length
Tan(Ф) = Opp / Adj
Tan(Ф) = 8 / 6
Ф = arcTan(8 / 6)
Ф ≈ 53.130°
now lets use that angle with one of the other trig functions to find the Hyp.. sin or cos will work b/c we have both the opp and the adj sides lengths. let's use cos
Cos(53.130) = 6 / Hyp
Hyp = 6 / Cos(53.130) ( I just used algebra to swap the two)
Hyp = 9.99997
the ladder will be 10' long.
ask in the comments if you need any more explaining
The number of feet in the length of the handrail is 17.3 ft.
The easiest way to see this is to imagine that we can "unfold" the spiral to create a rectangle
The bottom side of the rectangle is just the arc length of a circle with a radius of 3 ft turned through 270°= (3/4) of a whole revolution
(3/4) (2pi) (3) = (9/2)pi ft = 4.5 pi ft
The side of the rectangle will be the rise of the staircase = 10ft
And the diagonal of the rectangle will be the length of the handrail
We can use the Pythagorean Theorem to solve this
Handrail length = √ [ (4.5 pi)^2 + 10^2 ] ≈ 17.3 ft
Pythagorean theorem is the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
Learn more about the Pythagorean theorem here: brainly.com/question/343682
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Answer:
61
Step-by-step explanation:
you have to do 3 x 18 which is 54 then you have to add 7 which is 61
Answer:
Price of 1 adult ticket is <u>$10.8</u> and Price of 1 children ticket is <u>$5.4</u>.
Step-by-step explanation:
Given:
Number of adults = 2
Number of Children = 6
Total Amount of tickets sold = $54.
We need to find the price of one children's ticket and one adult ticket.
Solution:
Let the Cost of 1 adult ticket be 'x'.
Now Given:
Children tickets are on sale,half price of adult tickets.
Cost of 1 Children ticket =
Total Amount is equal to Number of adults multiplied by Cost of adult ticket plus Number of Children multiplied by Cost of Children ticket.
Framing in equation for we get;
Cost of 1 adult ticket = $10.8
Cost of 1 children ticket =
Hence Price of 1 adult ticket is <u>$10.8</u> and Price of 1 children ticket is <u>$5.4</u>.