Pls help due like- right on

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

the length of a diagonal of a square field is 220 metres find the length of a side in metres and the area of the field in hectar

andre [41]

Answer:

Step-by-step explanation:

h^2=x^2+y^2, since this is a square x=y=s so

220^2=2s^2

2s^2=48400

s^2=24200

s=24200^(1/2)m (exact)

s=155.56m (rounded to nearest hundredth of a meter)

One hectare is equal to 10000m^2

A=24200m^2(h/10000m^2)

A=2.42 hectares

7 0

2 years ago

If DM=45, what is the value of r?

amm1812

Answer:

15

Step-by-step explanation:

6 0

3 years ago

You want to draw a red then a blue marble. do you have a better chance of drawing a red then blue marble with or without replaci

elena-s [515]

Answer: Without replacing

Step-by-step explanation:

If you don't replace the first red marble, it decreases the number of red marbles in the mix, making the proportion of blue marbles relatively larger. For example, if there were 5 red and 5 blue marbles, there would be a 50% chance of drawing a blue marble. If the red drawn is not replaced, there is a 5/9 chance of drawing a blue marble, or a 55% chance of drawing one.

7 0

2 years ago

A prism is completely filled with 2304 cubes that have edge length of 14 cm

boyakko [2]

2304cubes(14^3 cm^3/cube)=6322176 cm^3

4 0

3 years ago

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