PLEASE HELP ME PLEASE HELP ME OUT WITH THIS THANK YOU

I need help with questions #7 and #8 plz

katen-ka-za [31]

Answer:

7. A = 40.8 deg; B = 60.6 deg; C = 78.6 deg

8. A = 20.7 deg; B = 127.2 deg; C = 32.1 deg

Step-by-step explanation:

Law of Cosines

$c^2 = a^2 + b^2 - 2ab \cos C$

You know the lengths of the sides, so you know a, b, and c. You can use the law of cosines to find C, the measure of angle C.

Then you can use the law of cosines again for each of the other angles. An easier way to solve for angles A and B is, after solving for C with the law of cosines, solve for either A or B with the law of sines and solve for the last angle by the fact that the sum of the measures of the angles of a triangle is 180 deg.

7.

We use the law of cosines to find C.

$18^2 = 12^2 + 16^2 - 2(12)(16) \cos C$

$324 = 144 + 256 - 384 \cos C$

$-384 \cos C = -76$

$\cos C = 0.2$

$C = \cos^{-1} 0.2$

$C = 78.6^\circ$

Now we use the law of sines to find angle A.

Law of Sines

$\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}$

We know c and C. We can solve for a.

$\dfrac{a}{\sin A} = \dfrac{c}{\sin C}$

$\dfrac{12}{\sin A} = \dfrac{18}{\sin 78.6^\circ}$

Cross multiply.

$18 \sin A = 12 \sin 78.6^\circ$

$\sin A = \dfrac{12 \sin 78.6^\circ}{18}$

$\sin A = 0.6535$

$A = \sin^{-1} 0.6535$

$A = 40.8^\circ$

To find B, we use

m<A + m<B + m<C = 180

40.8 + m<B + 78.6 = 180

m<B = 60.6 deg

8.

I'll use the law of cosines 3 times here to solve for all the angles.

Law of Cosines

$a^2 = b^2 + c^2 - 2bc \cos A$

$b^2 = a^2 + c^2 - 2ac \cos B$

$c^2 = a^2 + b^2 - 2ab \cos C$

Find angle A:

$a^2 = b^2 + c^2 - 2bc \cos A$

$8^2 = 18^2 + 12^2 - 2(18)(12) \cos A$

$64 = 468 - 432 \cos A$

$\cos A = 0.9352$

$A = 20.7^\circ$

Find angle B:

$b^2 = a^2 + c^2 - 2ac \cos B$

$18^2 = 8^2 + 12^2 - 2(8)(12) \cos B$

$324 = 208 - 192 \cos A$

$\cos B = -0.6042$

$B = 127.2^\circ$

Find angle C:

$c^2 = a^2 + b^2 - 2ab \cos C$

$12^2 = 8^2 + 18^2 - 2(8)(18) \cos B$

$144 = 388 - 288 \cos A$

$\cos C = 0.8472$

$C = 32.1^\circ$

8 0

3 years ago

Add -54 + 18. -36 -44 -72

Illusion [34]

Answer:

A. -36

*The answer must have a negative sign.*

Step-by-step explanation:

First, you had to add/subtract by the integers.

Then, you subtract by the numbers.

$54-18=36$

It change positive to negative sign.

$=-36$

Hope this helps!

-Charlie

Thank you!

8 0

3 years ago

Read 2 more answers

Solve each equation. Show your work 13a=-5 12−b=12.5 -0.1=-10c

amid [387]

1) 13a=-5
Make a the subject of the formula by dividing both sides by 13(the coefficient of a)
13a/13=-5/13
Therefore a= -0.385

The second one). 12-b= 12.5
You take the 12 to the other side making b subject of the formula (-b in this case)
-b= 12.5-12
-b= 0.5
(You cannot leave b with a negative sign so you will divide both sides by -1 to cancel out the negative sign)

-b/-1= 0.5/-1
Therefore b=-0.5

The third one). -0.1= -10c
You will divide both sides by the coefficient of c(number next to c) which is -10
-0.1/-10= -10c/-10

Hence, c= 0.01

5 0

3 years ago

P(more than z=-2.59)is?

romanna [79]

Neither p or z ISNT A NUMBER SO DO ONE WITH A NUMBER THAT QUESTIPON IS WRONG
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7 0

3 years ago

Jose wants to find the perimeter of triangle ABC. He uses the distance formula to determine the length of AC. Finish Jose’s calc

Vlad [161]

Answer:

15 units

Step-by-step explanation:

15.0

8 0

2 years ago