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lidiya [134]
3 years ago
15

A forest ranger in a 110 ft observation tower sees a fire. The angle of depression is 12 degrees. To the nearest foot, what is t

he distance from the tower to the fire?
Mathematics
1 answer:
Iteru [2.4K]3 years ago
7 0

The distance from the tower to the fire is 529.10feet

<h3>Angle of depression</h3>

The distance from the tower to the fire is the hypotenuse of the resulting triangle

Given the following

  • Height of the tower = 110ft

Using the SOH CAH TOA identity

sin theta = opp/hyp

sin 12 = 110/H

H = 110/sin12

H = 110/0.2079

H = 529.10

Hence the distance from the tower to the fire is 529.10feet

Learn more on SOH CAH TOA here: brainly.com/question/20734777

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4 years ago
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You have 8 gallons of lemonade to sell. You use cone-shaped cups that are 9 centimeters in diameter and 12 centimeters tall. Eac
andre [41]

You will need 119 cups to sell all of the lemonade.

Step-by-step explanation:

Given,

Diameter of cups = 9 cm

Radius of cup = \frac{Diameter}{2}=\frac{9}{2}=4.5\ cm

Height of cups = 12 cm

We will find volume of cup.

Volume = \frac{1}{3}\pi r^2h\\

Putting all the values

Volume=\frac{1}{3}(3.14)(4.5)^2(12)\\\\Volume=\frac{1}{3}(3.14)(20.25)(12)\\\\Volume= \frac{763.02}{3}\\\\Volume= 254.34\ cm^3

Therefore;

Each cup can hold 254.34 cubed centimeter of lemonade.

Number of gallons = 8

1 gallon = 3785 cm³

8 gallons = 3785*8 = 30280 cm³

Let,

x = Number of cups

Volume of lemonade in one cup * Number of cups = Volume of 8 gallons

254.34x=30280

Dividing both sides by 254.34

\frac{254.34x}{254.34}=\frac{30280}{254.34}\\x=119.05

Rounding off to nearest whole number

x = 119

You will need 119 cups to sell all of the lemonade.

Keywords: volume, division

Learn more about volume at:

  • brainly.com/question/1836777
  • brainly.com/question/1993757

#LearnwithBrainly

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3 years ago
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Answer:

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Step-by-step explanation:

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Answer:


Step-by-step explanation:

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