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mel-nik [20]
2 years ago
7

Given triangle ABC, A=105°, a=10cm, b=7cm, find B,C and c.

Mathematics
1 answer:
Whitepunk [10]2 years ago
4 0

The value of the side c will be 5.56 cm and angle C is 32.49° and angle B is 42.51°.

<h3>What is law of cosine?</h3>

Let there is a triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:

a² + b² – 2ab cos C = c²

Given triangle ABC, A = 105°, a = 10 cm, b = 7 cm.

Then we have

7² + c² – (2 · 7 · c) cos 105° = 10²

c² + 3.62c – 51 = 0

On solving, we have

c = 5.56

Then the angle C will be

10² + 7² – 2 · 7 · 10 · cos C = 5.56²

                149 – 140 cos C = 30.91

                                 cos C = 0.8435

                                        C = 32.49°

We know that

       ∠A + ∠B + ∠C = 180°

105° + ∠B + 32.49° = 180°

                         ∠B = 42.51°

Learn more about law of cosines here:

brainly.com/question/17289163

#SPJ1

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Find the mean, the median, and all modes for the data in the given frequency distribution. (Round your answers to one decimal pl
kvasek [131]

Answer: Mean = 7.8

              Median = 9

             Mode = 2,9

Step-by-step explanation: <u>Mean</u> is the average value of a data set. Mean from a frequency table is calculated as:

E(X)=\frac{2(10)+3(9)+9(10)+11(7)+12(3)+15(4)+16(3)}{10+9+10+7+3+4+3}

E(X) = 7.8

Mean for the given frequency distribtuion is 7.8.

<u>Median</u> is the central term of a set of numbers. Median in a frequency table is calculated as:

1) Find total number, n:

n = 10 + 9 + 10 + 7 + 3 + 4 + 3 = 46

2) Find position, using: \frac{n+1}{2}

\frac{n+1}{2}=\frac{47}{2} = 23.5

Median is in the 23.5th position.

3) Find the position by adding frequencies: for this frequency distribution, 23.5th position is 9

Median for this frequency distribution is 9.

<u>Mode</u>  is the number or value associated with the highest frequency.

In this frequency distribution, 2 and 9 points happen 10 times. So, mode is 2 and 9.

Mode for this distribution is 2 and 9.

7 0
3 years ago
Michael walks his black lab 6 2/3 miles every week. If he walks his dog every Monday, Wednesday, Friday, and Sunday. How many mi
Elenna [48]

Answer: 1.7 miles

Step-by-step explanation:

dog is walked four times a week

6 2/3 miles in all

6 2/3 divided by 4 = 1.66666667

1.66666667 rounded to nearest tenth = 1.7

6 0
3 years ago
Guys look at the pic of the park and read the question I need this ASAP WITH ALL STEPS the choices are
Alik [6]

Answer:

A. 821.5 Square Yards

Step-by-step explanation:

30 x 30= 900

900 is the area for the whole park

To find the pool area you need to do pi times Radius squared

so 3.14 x 5 x 5

That equals 78.5 for the pool area.

So to find the grass area you need to subtract the pool area from the park

900 - 78.5 = 821.5 square yards!

5 0
3 years ago
The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2 cm^2/
VARVARA [1.3K]

Answer:

The base is decreasing at 2 cm/min.

Step-by-step explanation:

The area (A) of a triangle is given by:

A = \frac{1}{2}bh   (1)

Where:

b: is the base

h: is the altitude = 10 cm

If we take the derivative of equation (1) as a function of time we have:

\frac{dA}{dt} = \frac{1}{2}(\frac{db}{dt}h + \frac{dh}{dt}b)

We can find the base by solving equation (1) for b:

b = \frac{2A}{h} = \frac{2*120 cm^{2}}{10 cm} = 24 cm

Now, having that dh/dt = 1 cm/min, dA/dt = 2 cm²/min we can find db/dt:

2 cm^{2}/min = \frac{1}{2}(\frac{db}{dt}*10 cm + 1 cm/min*24 cm)

\frac{db}{dt} = \frac{2*2 cm^{2}/min - 1 cm/min*24 cm}{10 cm} = -2 cm/min    

         

Therefore, the base is decreasing at 2 cm/min.

               

I hope it helps you!  

7 0
2 years ago
Look at this set of 10 numbers:
swat32
In the original set of numbers, the median is six
But, if six was added to the set, then the median would be six
So the median wouldn't decrease at all
8 0
3 years ago
Read 2 more answers
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