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4 years ago

Find the range for the measurement of the third side of a triangle, x, given the measures of the two sides: 5m and 11m.

Mathematics

1 answer:

Sedbober [7]4 years ago

4 0

C is more than 6 less than 16

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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

You don’t know how important this is Please help me!!

Natali5045456 [20]

Answer:

f(x)= $\frac{7}{5}$ x- $\frac{6}{5}$

Step-by-step explanation:

First put 7x-5y=6 into slope intercept form

y= $\frac{7}{5}$ x- $\frac{6}{5}$

Then put it into f(x) form

7 0

3 years ago

katrin2010 [14]

Answer:

A ≈ 35.3 units²

Step-by-step explanation:

Calculate the radius CB using Pythagoras' identity in the right triangle.

CB² + AB² = AC²

CB² + 6² = 9²

CB² + 36 = 81 ( subtract 36 from both sides )

CB² = 45 = r²

Then area of quarter circle is

A = $\frac{1}{4}$ × πr² = $\frac{1}{4}$ × π × 45 ≈ 35.3

6 0

3 years ago

A carpet installer charges a flat rate of $40, plus $1.50 per square foot for labor. So, the total cost for labor depends on the

Lina20 [59]

Answer:

The total cost will be $40 plus $1.50 per square foot of carpet or $40+$1.50x

3 0

3 years ago

Read 2 more answers

Find the circumference in feet.

Rama09 [41]

Answer:

C≈25.13ft

Step-by-step explanation:

Using the formulas

C=2πr

d=2r

Solving for C

C=πd=π·8≈25.13274ft

3 0

3 years ago