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2 years ago

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HELP ASAP I WILL MARK BRAINLEST

1 answer:

Zanzabum2 years ago

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We need to know what u need help with

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

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

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

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

$100 = 180 - 144 *Cos\alpha$

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

3 years ago

For the function f(x)=(7-8x)^2, find f^-1 determine whether f^-1 is a function

sertanlavr [38]

Is this question correct ?

5 0

3 years ago

A tennis ball is in a cylindrical container. The ball has a radius of 5 inches and the cylinder has a height of 8 inches. How mu

Nostrana [21]

Answer:

104.7 in^3

Step-by-step explanation:

Step one:

given data

The ball has a radius of 5 inches and

the cylinder has a height of 8 inches

Step two:

The volume of the cylinder

$v= \pi r^2 h$

substitute our data

$v= 3.142*5^2*8\\\\v=628.4in^3$

The volume of the ball

$v=4/3 \pi r^3$

substitute our data

$v= 4/3 *3.142*5^3\\\\v= 523.7 in^3$

The space will have a volume of

=628.4-523.7

=104.7 in^3

7 0

2 years ago

Since I can not upload test can you answer this homework question for me thanks!

madam [21]

Answer:

The answer just so happens to be 6!

7 0

3 years ago

Dr. Campbell put 3.456 ounces of pills into bottles. She put 0.036 ounce of pills into each bottle. How many bottles did Dr. Cam

bija089 [108]

Answer:

c) 96

Step-by-step explanation:

3.456÷ 0.036

the answer is 96

4 0

2 years ago

Read 2 more answers