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k0ka [10]
4 years ago
15

The rattler roller coaster is 66 ft tall. if you are at the top of the roller coaster and your friend larry is on the ground 35

ft away from the base of the coaster, what is the angle of depression from the top of the roller coaster to the spot where larry is standing? round to the nearest hundredth.

Mathematics
1 answer:
bogdanovich [222]4 years ago
5 0
Use ratio of tan to find the angle of depression
tan of an angle = side in front of the angle / side adjacent to the angle

Plug in the numbers
tan α = 35/66
α = arctan (35/66)
α = 27.937...
to the nearest hundredth
α = 27.94°

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The area of the shaded region is  \rm (150\sqrt{3} \ - 75\pi ) \ feet^2 option first is correct.

It is given that a circle is inscribed in a regular hexagon with sides of 10 feet.

It is required to find the shaded area (missing data is attached shown in the picture).

<h3>What is a circle?</h3>

It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).

We have a hexagon with a side length of 10 feet.

We know the area of the hexagon is given by:

\rm A = \frac{3\sqrt{3} }{2} a^2  where a is the side length.

\rm A = \frac{3\sqrt{3} }{2} 10^2 ⇒ 150\sqrt{3} \rm feet^2

We have the shortest length = x feet and from the figure:

2x = 10

x = 5 feet

The radius of the circle r = longer leg

\rm r = x\sqrt{3} \Rightarrow 5\sqrt{3} feet

The area of the circle a = \pi r^2  ⇒ \pi (5\sqrt{3} )^2 \Rightarrow 75\pi \ \rm feet^2  

The area of the shaded region = A - a

\rm =(150\sqrt{3} \ - 75\pi ) \ feet^2

Thus, the area of the shaded region is  \rm (150\sqrt{3} \ - 75\pi ) \ feet^2

Learn more about circle here:

brainly.com/question/11833983

7 0
2 years ago
What is the answer to this?
fredd [130]

Answer:

y = 3, TU = 6

Step-by-step explanation:

SU is an angle bisector and divides the opposite side into segments that are proportional to the other 2 sides, that is

\frac{SV}{ST} = \frac{VU}{TU} , substitute values

\frac{24}{4y-2} = \frac{14.4}{2y} ( cross- multiply )

14.4(4y - 2) = 48y

57.6y - 28.8 = 48y ( subtract 48y from both sides )

9.6y - 28.8 = 0 ( add 28.8 to both sides )

9.6y = 28.8 ( divide both sides by 9.6 )

y = 3

Then

TU = 2y = 2 × 3 = 6

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