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3 years ago

Will mark brainliest!!

Mathematics

1 answer:

iogann1982 [59]3 years ago

7 0

Answer:

the angle is 176

Step-by-step explanation:

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There are 3 islands A,B,C. Island B is east of island A, 8 miles away. Island C is northeast of A, 5 miles away and northwest of

Nostrana [21]

Answer:

The bearing needed to navigate from island B to island C is approximately 38.213º.

Step-by-step explanation:

The geometrical diagram representing the statement is introduced below as attachment, and from Trigonometry we determine that bearing needed to navigate from island B to C by the Cosine Law:

$AC^{2} = AB^{2}+BC^{2}-2\cdot AB\cdot BC\cdot \cos \theta$ (1)

Where:

$AC$ - The distance from A to C, measured in miles.

$AB$ - The distance from A to B, measured in miles.

$BC$ - The distance from B to C, measured in miles.

$\theta$ - Bearing from island B to island C, measured in sexagesimal degrees.

Then, we clear the bearing angle within the equation:

$AC^{2}-AB^{2}-BC^{2}=-2\cdot AB\cdot BC\cdot \cos \theta$

$\cos \theta = \frac{BC^{2}+AB^{2}-AC^{2}}{2\cdot AB\cdot BC}$

$\theta = \cos^{-1}\left(\frac{BC^{2}+AB^{2}-AC^{2}}{2\cdot AB\cdot BC} \right)$ (2)

If we know that $BC = 7\,mi$ , $AB = 8\,mi$ , $AC = 5\,mi$ , then the bearing from island B to island C:

$\theta = \cos^{-1}\left[\frac{(7\mi)^{2}+(8\,mi)^{2}-(5\,mi)^{2}}{2\cdot (8\,mi)\cdot (7\,mi)} \right]$

$\theta \approx 38.213^{\circ}$

The bearing needed to navigate from island B to island C is approximately 38.213º.

8 0

3 years ago

A theatre has seats arranged in rows of 24, 382 people attend a show at the theatre. What is the smallest number of rows that is

kipiarov [429]

Answer:

A minimum of 16 rows are needed

Step-by-step explanation:

Here, we want to calculate the number of rows minimum that could seat 382 people in rows of 24 seats.

Mathematically, what we need to do here is to make a division.

We shall divide the number of people by the number of seats in a row so that we can get the number of rows needed.

Mathematically, that would be; 382/24 = 15 22/24

We are looking at a minimum number.

So we can see that 15 rows will be filled, with an extra 22 seats in the next row leaving only 2 seats in the next row unoccupied.

So we can see that the minimum number of rows required is 16 rows

3 0

4 years ago

a globe has a diameter of 12 inches. it fits inside a cube-shaped box that has a side length of 12 inches. What is the volume, r

baherus [9]

Answer:

823.68 inches

Step-by-step explanation:

7 0

3 years ago

I NEED HELP! Find the distance from(-4,4) to the line defined by y= -2x+6.Express as a radical or a number rounded to the neares

marysya [2.9K]

In radical form, the shortest distance from ( -4 , 4 ) and the line y = -2x + 6 is 2√5 units.

Attached below is the calculation to arrive at the answer as well as a graph.

8 0

3 years ago

Is 3 a divisor of 51?

Mariulka [41]

Answer:
Yes

Step by step explanation

5 0

3 years ago

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