What is the 6th term of the sequence?

Solve the oblique triangle where side a has length 10 cm, side c has length 12 cm, and angle beta has measure thirty degrees. Ro

Ugo [173]

Answer:

$Side\ B = 6.0$

$\alpha = 56.3$

$\theta = 93.7$

Step-by-step explanation:

Given

Let the three sides be represented with A, B, C

Let the angles be represented with $\alpha, \beta, \theta$

[See Attachment for Triangle]

$A = 10cm$

$C = 12cm$

$\beta = 30$

What the question is to calculate the third length (Side B) and the other 2 angles ( $\alpha\ and\ \theta$ )

Solving for Side B;

When two angles of a triangle are known, the third side is calculated as thus;

$B^2 = A^2 + C^2 - 2ABCos\beta$

Substitute: $A = 10$ , $C =12$ ; $\beta = 30$

$B^2 = 10^2 + 12^2 - 2 * 10 * 12 *Cos30$

$B^2 = 100 + 144 - 240*0.86602540378$

$B^2 = 100 + 144 - 207.846096907$

$B^2 = 36.153903093$

Take Square root of both sides

$\sqrt{B^2} = \sqrt{36.153903093}$

$B = \sqrt{36.153903093}$

$B = 6.0128115797$

$B = 6.0$ <em>(Approximated)</em>

Calculating Angle $\alpha$

$A^2 = B^2 + C^2 - 2BCCos\alpha$

Substitute: $A = 10$ , $C =12$ ; $B = 6$

$10^2 = 6^2 + 12^2 - 2 * 6 * 12 *Cos\alpha$

$100 = 36 + 144 - 144 *Cos\alpha$

$100 = 180 - 144 *Cos\alpha$

Subtract 180 from both sides

$100 - 180 = 180 - 180 - 144 *Cos\alpha$

$-80 = - 144 *Cos\alpha$

Divide both sides by -144

$\frac{-80}{-144} = \frac{- 144 *Cos\alpha}{-144}$

$\frac{-80}{-144} = Cos\alpha$

$0.5555556 = Cos\alpha$

Take arccos of both sides

$Cos^{-1}(0.5555556) = Cos^{-1}(Cos\alpha)$

$Cos^{-1}(0.5555556) = \alpha$

$56.25098078 = \alpha$

$\alpha = 56.3$ <em>(Approximated)</em>

Calculating $\theta$

Sum of angles in a triangle = 180

Hence;

$\alpha + \beta + \theta = 180$

$30 + 56.3 + \theta = 180$

$86.3 + \theta = 180$

Make $\theta$ the subject of formula

$\theta = 180 - 86.3$

$\theta = 93.7$

5 0

2 years ago

What is the equation of the function in slope-intercept form?

Rasek [7]

To write this equation, you need use the formula y=mx+b.

m represents the slope and b represents the y intercept.

The y intercept is the point where the line touches the y axis. In this case, the y-intercept is 1.

The slope is just rise over run from one coordinate to another. The slope is 2/-1 which could be simplified as -2. The slope just means that we are going up 2 and left 1 to get to a new coordinate.

The equation is y=-2x+1

Have a good day! :)

7 0

2 years ago

The ratio of boys to girls in a class is 5:3. There are 32 students in the class. How many students are boys?

yan [13]

Answer: There are 20 boys

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

A line passes through the point (-2, 4), and its y-intercept is (0,6). What is the equation of the line that is

MatroZZZ [7]

Answer:

y = -x + 9

Step-by-step explanation:

The line that passes through the points (-2,4) and (0,6) has a slope of 1, and a y intercept of 6. The equation to the first line is y = x + 6. and perpendicular lines always have the opposite, reciprocal slope of the other line. So the slope for the second line would be -1. A line with the slope of -1 and a point of (5,4) would contain the points (5,4) , (4,5) , (3,6) , (2,7) , (1,8) , and (0,9) , which is the y intercept for the second line. So the equation for the second line would be y = -x + 9

8 0

2 years ago

The sets of numbers 3, 4, 5 and 8, 15, 17 are Pythagorean triples. Use what you know about the Pythagorean Theorem and explain o

konstantin123 [22]

Answer:

When we have 3 numbers, like:

a, b and c.

Such that:

a < b < c.

These numbers are a Pythagorean triplet if the sum of the squares of the two smaller numbers, is equal to the square of the larger number:

a^2 + b^2 = c^2

This is equivalent to the Pythagorean Theorem, where the sum of the squares of the cathetus is equal to the hypotenuse squared.

Now that we know this, we can check if the given sets are Pythagorean triples.

1) 3, 4, 5

Here we must have that:

3^2 + 4^2 = 5^2

solving the left side we get:

3^2 + 4^2 = 9 + 16 = 25

and the right side:

5^2 = 25

Then we have the same in both sides, this means that these are Pythagorean triples.

2) 8, 15, 17

We must have that:

8^2 + 15^2 = 17^2

Solving the left side we have:

8^2 + 15^2 = 64 + 225 = 289

And in the right side we have:

17^2 = 17*17 = 289

So again, we have the same result in both sides, which means that these numbers are Pythagorean triples

4 0

2 years ago