Write an equation of the line in point slop form that passes through the two given points

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

at the playground, the new sandbox was 3 meters wide and 2 meters long. what is the area of the sandbox

S_A_V [24]

area = length times width

area = 2 meters * 3 meters

area = 6 m^2

3 0

4 years ago

Read 2 more answers

Which equation is equivalent to<br><br> f(x) = 16x4 – 81 = 0?

Vesna [10]

Answer:

The equivalent expression is:

$16x^4-81=(4x^2-9)(4x^2+9)$

Step-by-step explanation:

We have been given the equation:

$f(x)=16x^4-81=0$

Equivalent expression can be computed by solving the expression ai its maximum.

We can factorize the given equation:

By using $a^2-b^2=(a+b)(a-b)$

Here, $a=4x^2,b=9$

Hence, we get the equation below:

$16x^4-81=(4x^2-9)(4x^2+9)$

Therefore, the equivalent expression is:

$16x^4-81=(4x^2-9)(4x^2+9)$

5 0

4 years ago

Read 2 more answers

How do you do simplify this -9 -11

zheka24 [161]

Answer:

-9 + -11=-20

Step-by-step explanation:

Since subtracting is the same as addition of the oppositie, just putting a negative symbol is easier because you are only working with negative numbers, instead of one negative and one positive.

Did that help?

7 0

3 years ago

Read 2 more answers

A football team gains 11 yards on a pass, loses 8 yards in a sack,

OLEGan [10]

Answer:

Step-by-step explanation:

loose (8+5) yards so they lost 13 yards

and obviously they gained 11 yards according to the information given.

5 0

3 years ago