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3 years ago

What is the value of a° in the figure shown below?

Mathematics

1 answer:

VMariaS [17]3 years ago

3 0

The answer would be 18 because if you put 3a+6a+a=180 (the degrees of a triangle) and solve it a becomes 18

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

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

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

$100 = 180 - 144 *Cos\alpha$

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

A fully loaded and fueled spacecraft can weigh close to million pounds. What is this weight converted to tons?

Dafna1 [17]

Answer:

The answer is 500 pounds

3 0

3 years ago

Which equation is in standard form?

kifflom [539]

I believe that the last one is true

because the linear equations are

y=ax+b

which means that the point of y-axis is on one side and the slope, point on x-axis and y-intercept are on the other side

good luck

6 0

3 years ago

Read 2 more answers

What is the value of d? Assume that the line is a tangent to the circle.

motikmotik

We have been given a chord and tangent to a circle. We have been minor arc measure that is equal to $118^{0}$ .

Since we know that angle formed by a secant and tangent of circle is half of the measure of intercepted arc.

$\measuredangle x=\frac{1}{2}m \widehat{ABC}$

We can find intercepted arc by subtracting minor arc measure from 360 degrees because minor and major arcs add up to 360 degrees.

$360^{0}-118^{0}=242^{0}$

Now we will plug given values in our formula,

$d^{0}=\frac{242}{2}=121$

Therefore, the measure of d is 121 degrees.

5 0

3 years ago

Read 2 more answers

I NEED THE ANSWER AS SOON AS POSSIBLE PLEASE!!

Anit [1.1K]

Answer:

$\Large \boxed{\sf \ \ 4\sqrt{a^2+b^2} \ \ }$

Step-by-step explanation:

Hello,

You can use Pythagoras in the 4 right triangles.

For one triangle it comes $\sqrt{a^2+b^2}$ .

Then for the polygon it gives $4\cdot \sqrt{a^2+b^2}$ .

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

5 0

3 years ago