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guapka [62]
3 years ago
11

A boat is sighted from a 50-meter observation tower on the shoreline at an angle of depression of 4 degrees moving directly towa

rds the shore at a constant speed. Five minutes later the angle of depression of the boat is 12 degrees. What is the speed of the boat in kilometers per hour?
Mathematics
1 answer:
MAXImum [283]3 years ago
4 0

Answer:

  5.76 km/h

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relationship between angles and sides of a right triangle. Here, we are given the side opposite the angle (angle of depression), and we want to find the adjacent side (distance from shore).

  Tan = Opposite/Adjacent

  tan(4°) = (height of tower)/(distance from shore)

  tan(4°) = (50 m)/(distance from shore)

Then the distance from shore is ...

  distance from shore = (50 m)/tan(4°) ≈ 715.03 m

__

At the second sighting, the distance from shore is ...

  distance from shore = (50 m)/tan(12°) ≈ 235.23 m

So, the distance traveled in 1/12 hour is ...

  715.03 m - 235.23 m = 479.80 m

and the speed in km per hour is ...

  speed = 0.4798 km/(1/12 h) = 5.7576 km/h

The speed of the boat is about 5.76 km per hour.

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1. 208/x = 100/130
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8 0
3 years ago
It takes a train 60 seconds to completely drive through a bridge of 1260 m, and 90 seconds to completely drive through a tunnel
Olegator [25]

The length of train is 120 meters

The speed of train is 25 meter per second

<u><em>Solution:</em></u>

The speed is given by formula:

speed = \frac{distance}{time}

Given that,

It takes a train 60 seconds to completely drive through a bridge of 1260 m

And 90 seconds to completely drive through a tunnel of 2010 m

Let the length of the train be "x"

<em><u>The total distance travelled by the train across the bridge is given by:</u></em>

total distance = x + 1260 + x = 2x + 1260

[ here we use x + x to represent that train completely drives through bridge ]

The time taken is given as 60 seconds

<em><u>Therefore, the speed is given as:</u></em>

speed = \frac{2x+ 1260}{60}

<em><u>The total distance travelled by the train through the tunnel is given by:</u></em>

total distance = x + 2010 + x = 2x + 2010

The time taken is given as 90 seconds

<em><u>Therefore, the speed is given as:</u></em>

speed = \frac{2x+ 2010}{90}

The speed of the train was the same in both cases.

Equate both speeds

\frac{2x+ 1260}{60} = \frac{2x+ 2010}{90}

\frac{x+630}{30} = \frac{x+1005}{45}

45(x+630) = 30(x+1005)\\\\45x + 28350 = 30x + 30150\\\\45x - 30x = 30150 - 28350\\\\15x = 1800\\\\x = 120

Thus length of train is 120 meters

<em><u>Find the speed of train:</u></em>

speed = \frac{2x+ 1260}{60}\\\\speed = \frac{2(120) + 1260)}{60}\\\\speed = 25

Thus speed of train is 25 meter per second

5 0
3 years ago
What is the measure of T and U
andreev551 [17]
T-> 180-2*(54)= 72° ……
5 0
3 years ago
ILL GIVE BRAINLIEST TO THE CORRECT ANSER BUT ANSWER ASAP
gulaghasi [49]

Answer:

12 and 13

Step-by-step explanation:

I hope this helps! Have a lovely day!! :)

4 0
2 years ago
Read 2 more answers
Maggie's brother is 4 years younger than four times her age. The sum of their ages is 26.
Gelneren [198K]

Answer:

Maggie is 6 years old

Step-by-step explanation:

M + B = 26

B = 26 - M

4M - 4 = B

4M - 4 = 26 - M

5M = 30

M = 6

Maggie is 6 years old

3 0
3 years ago
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