1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Verizon [17]
3 years ago
8

Use the Law of Cosines to find the values of x and y. (PLEASE HELPPP!!!!)

Mathematics
1 answer:
vredina [299]3 years ago
7 0

Answer:

x = 49.8^\circ\\y = 54.6^\circ

Step-by-step explanation:

Kindly refer to the image attached in the answer region for labeling of triangle.

<em>AB </em><em>= 16 </em>

<em>BC </em><em>= 19</em>

<em>AC </em><em>= 15 </em>

\angle ABC = x^\circ\\\angle ACB = y^\circ

We have to find the <em>angles </em><em>x</em> and <em>y</em> i.e. \angle B \text{ and }\angle C.

Formula for <em>cosine rule</em>:

cos B = \dfrac{a^{2}+c^{2}-b^{2}}{2ac}

Where  

<em>a</em> is the side opposite to \angle A,

<em>b</em> is the side opposite to \angle B  and

<em>c</em> is the side opposite to \angle C.

\Rightarrow cos x = \dfrac{19^{2}+16^{2}-15^{2}}{2 \times 19 \times 16}\\\Rightarrow cos x = \dfrac{392}{608} \\\Rightarrow x = 49.8^\circ

Similarly, for finding the value of <em>y:</em>

cos C = \dfrac{a^{2}+b^{2}-c^{2}}{2ab}\\\Rightarrow cos y = \dfrac{19^{2}+15^{2}-16^{2}}{2  \times 19 \times 15}\\\Rightarrow cos y = \dfrac{330}{570}\\\Rightarrow y = 54.6^\circ

Hence, the values are:

x = 49.8^\circ\\y = 54.6^\circ

You might be interested in
The sides of a triangle are in the ratio 3 : 4 : 5. What is the length of each side if the perimeter of the triangle is 90 cm
svet-max [94.6K]
The sides of the triangle are 3x, 4x and 5x

3x + 4x + 5x = 90
12x = 90
x = 90/12
x = 7.5

first side = 3x = 3 * 7.5 = 22.5 cm
second side = 4x = 4 * 7.5 = 30 cm
third side = 5x = 5*7.5 = 37.5 cm
7 0
3 years ago
12. The ratio of clown fish to angelfish at a pet store is 5:4. The ratio of
777dan777 [17]

Answer:

a. There are 48 angelfish.

b. There are 36 goldfish.

Step-by-step explanation:

the ration of clownfish to angelfish is 5:4 and there are 60 clownfish.

60:? 5x=60 x=12 12(4)=48

60:48 there are 48 angelfish

the ration of angelfish to goldfish is 4:3 and know we know there are 48 angelfish

48:? 4x=48 x=12 12(3)=36

48:36 there are 36 goldfish

4 0
3 years ago
Read 2 more answers
A farmer had 1,000 horses and cows. After selling some of them, he had 550 horses and 350 cows left. How many horses and cows di
ipn [44]
The farmer had sold 100 horses and cows
5 0
2 years ago
A line passes through the points
masha68 [24]

Answer:

y=-2x+7

enter the point into point slope form to find the slope and then use one of the points in point slope form  and rearrange it to have y by itself

4 0
3 years ago
Marisol is being paid $792 to provide nutrition counseling, It took her 8 hours more than she expected, so
olchik [2.2K]

Answer: 44 hours.

Step-by-step explanation:

Marisol is being paid $792.

We know that the job took her 8 hours more than she expected, so if we define T as the time she expected, this job took her:

T + 8 hours.

The amount of money per hour that she expected is calculated as:

$792/T = X

And for those 8 extra hours, she won $4 less per hour, then we have:

$792/(T + 8hs) = X - $4

Then we have a system of equations:

$792/T = X

$792/(T + 8hs) = X - $4

To solve this, we can notice that in the first equation X is isolated, then we could replace that in the second equation to get:

$792/(T + 8hs) = $792/T - $4

Now we can solve this for T.

$792 = ($792/T - $4)*(T + 8hs)  = $792 + $792*(8hs/T) - $4*T + $32*hs

0 = $792*(8hs/T) - $4*T + $32*hs

Let´s multiply this both sides by T

0*T = ($792*(8hs/T) - $4*T + $32*hs)*T

0 = $792*8hs - $4*T^2 +$32*T*hs

This is a quadratic equation, where i will write this witout units so it is easier to read and follow:

0 = -4*T^2 + 32*T + 792*8

The solutions cab be found by using the Bhaskara´s formula, these are:

T = \frac{-32 +- \sqrt[2]{(32^2 - 4*(-4)*(792*8)} }{2*-4}  = \frac{-32 +-320}{-8}

Then the solutions are:

T = (-32 + 320)/-8 = -36 hours (This is a negative time, and it does not really have a meaning in this problem, so we can discard this option)

The other solution is:

T = (-32 - 320)/-8 = 44 hours.

Then we can conclude that she expected the job would take 44 hours in total.

5 0
2 years ago
Other questions:
  • Mulch to cover a rectangle garden cost $48. Mulch is needed to cover a larger,similar garden. the ratio of dimensions 2:3. how m
    8·1 answer
  • The scatter plot below shows the relationship between the diameter (x), in mm, and mass f(x), in grams, of a berry: ordered pair
    14·1 answer
  • Please help me with this
    13·1 answer
  • Please help urgent ! trig !
    11·1 answer
  • X-8pi=pi<br><br><br> plz help (i couldnt find the pi button )
    12·1 answer
  • I need help. This is due today
    13·1 answer
  • If a data plot has most of the data on the left side of the graph, and a tail to the right, what do we call it?
    9·1 answer
  • PLEASE HELP ME!!!! I NEED TO TURN IN THIS IN 15 MINUTES
    5·1 answer
  • A 21 foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground if 14 f
    7·1 answer
  • Please answer today, I will give brainly crown when I can :)
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!