All categories

2 years ago

In triangle ABC, a=31 , b=22 , c=18. Identify m∠A rounded to the nearest degree.

Mathematics

1 answer:

Veronika [31]2 years ago

8 0

Answer:

101

Step-by-step explanation:

According to the Law of Cosines, for any △ABC with side lengths a, b, and c, a2=b2+c2−2bccosA; b2=a2+c2−2accosB; and c2=a2+b2−2abcosC

The Law of Cosines can be used because all three side lentghs are known.

Set up the equation for the Law of Cosines:

a2=b2+c2−2bccosA

Substitute the known values into the Law of Cosines:

312=222+182−2(22)(18)cosA

Square the values and multiply:

961=484+324−792cosA

Add:

961=808−792cosA

Subtract 808

from both sides:

153=−792cosA

Divide both sides by −792

153−792=cosA

According to this equation m∠A

is equal to the inverse cosine function of −153792

. Write this:

m∠A=cos−1(−153792)

Calculate the value of the inverse cosine −153792

on a calculator:

m∠A≈101°

Therefore, m∠A≈101°

You might be interested in

(d)

mash [69]

Answer: The 4 answers are x=18, x=3, x=48, x=81 1/2.

Step-by-step explanation: Isolate the variable by dividing by each side by factors that don't contain the variable.

6 0

2 years ago

Please help! Need to confirm my answers.

MariettaO [177]

Answer:

Step-by-step explanation:

Average rate of change is Δy / Δx.

For f(x):

[ f(1) - f(0) ] / (1 - 0)

(1 - 3) / (1 - 0)

-2

For g(x):

[ g(1) - g(0) ] / (1 - 0)

(4 - 3) / (1 - 0)

6 0

3 years ago

I don’t know how to solve for Q.

Naya [18.7K]

Answer:

∠Q = 75°

Step-by-step explanation:

Start by recognizing that the triangle is isosceles (the long sides are marked as being equal-length). That means angles Q and R have the same measure.

Next, you use the fact that the sum of angles is 180° to write an equation.

∠R +∠P +∠Q = 180°

(2x +15)° +x° +(2x +15)° = 180° . . . . substitute the known values

5x +30 = 180 . . . . . . . . . . . . . . . . divide by °, collect terms

5x = 150 . . . . . . . . subtract 30

x = 30 . . . . . . . divide by 5

Then angle Q is ...

∠Q = (2x +15)° = (2×30 +15)°

∠Q = 75°

8 0

2 years ago

Find the volume of a spere with radius of 7

choli [55]

Formula for volume of sphere V = 4/3 (Pi) r^3, where Pi ~ 3.14 and r is the radius = 7.

Therefore V = 4/3 * 3.14 * 7^3

= 4/3 * 3.14 * 343

= 4/3 * 1077.02

= 1,436.02667 cubic units

6 0

3 years ago

Read 2 more answers

Kelsey makes pendants that she would like to sell at an upcoming craft fair. She must pay $200 to rent a booth at the craft fair

lubasha [3.4K]

Answer:

Additional <em>26</em> pendants are to be sold to make profit.

Step-by-step explanation:

Rent of booth at the craft fair = $200

Cost of material for each pendant = $7.80

Let Kelsey makes $x$ number of pendants.

To calculate the total spending, we have to add the rent of booth at the craft fair and cost of material for $x$ number of pendants.

Cost of material for $x$ number of pendants = Cost of material for each pendant multiplied by number of pendants

Cost of material for $x$ number of pendants = $7.80 $\times$ $x$

So, total cost = $200 + $7.80 $\times$ $x$

Now, each pendant is sold at $13.50

So, total money made by selling $x$ pendants = $13.50 $\times$ $x$

For making profit, total money made must be greater than the total cost.

Therefore, the inequality becomes:

$\bold{13.50 \times x > 200+7.80\times x }$

Let us solve the inequality now:

$13.50x - 7.80x>200\\\Rightarrow 5.7x > 200\\\Rightarrow \bold{x > 35.08}$

So, at least 36 pendants are to be sold to make a profit.

Additional 36-10 = <em>26</em> pendants are to be sold to make profit.

5 0

3 years ago