1/5 of 45 is what number?

HELP ME PLEASE!!! I DON'T UNDERSTAND!

Rama09 [41]

Answer: 12

Step-by-step explanation:

this is a right angled triangle so you use the pythagorean theory

which is a^2 + b^2 = c^2

you have c and b already. c is the hypotenuse.

a^2 + 16^2 = 20^2

a^2 + 256 = 400

a^2 = 400 - 256

a^2 = 144

then you square root 144 and get..

a = 12

3 0

3 years ago

Read 2 more answers

Please dont ignore, Need help!!! Use the law of sines/cosines to find..

Ket [755]

Answer:

16. Angle C is approximately 13.0 degrees.

17. The length of segment BC is approximately 45.0.

18. Angle B is approximately 26.0 degrees.

15. The length of segment DF "e" is approximately 12.9.

Step-by-step explanation:

By the law of sine, the sine of interior angles of a triangle are proportional to the length of the side opposite to that angle.

For triangle ABC:

$\sin{A} = \sin{103\textdegree{}}$ ,
The opposite side of angle A $a = BC = 26$ ,
The angle C is to be found, and
The length of the side opposite to angle C $c = AB = 6$ .

$\displaystyle \frac{\sin{C}}{\sin{A}} = \frac{c}{a}$ .

$\displaystyle \sin{C} = \frac{c}{a}\cdot \sin{A} = \frac{6}{26}\times \sin{103\textdegree}$ .

$\displaystyle C = \sin^{-1}{(\sin{C}}) = \sin^{-1}{\left(\frac{c}{a}\cdot \sin{A}\right)} = \sin^{-1}{\left(\frac{6}{26}\times \sin{103\textdegree}}\right)} = 13.0\textdegree{}$ .

Note that the inverse sine function here $\sin^{-1}()$ is also known as arcsin.

By the law of cosine,

$c^{2} = a^{2} + b^{2} - 2\;a\cdot b\cdot \cos{C}$ ,

where

$a$ , $b$ , and $c$ are the lengths of sides of triangle ABC, and
$\cos{C}$ is the cosine of angle C.

For triangle ABC:

$b = 21$ ,
$c = 30$ ,
The length of $a$ (segment BC) is to be found, and
The cosine of angle A is $\cos{123\textdegree}$ .

Therefore, replace C in the equation with A, and the law of cosine will become:

$a^{2} = b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}$ .

$\displaystyle \begin{aligned}a &= \sqrt{b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}}\\&=\sqrt{21^{2} + 30^{2} - 2\times 21\times 30 \times \cos{123\textdegree}}\\&=45.0 \end{aligned}$ .

For triangle ABC:

$a = 14$ ,
$b = 9$ ,
$c = 6$ , and
Angle B is to be found.

Start by finding the cosine of angle B. Apply the law of cosine.

$b^{2} = a^{2} + c^{2} - 2\;a\cdot c\cdot \cos{B}$ .

$\displaystyle \cos{B} = \frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}$ .

$\displaystyle B = \cos^{-1}{\left(\frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}\right)} = \cos^{-1}{\left(\frac{14^{2} + 6^{2} - 9^{2}}{2\times 14\times 6}\right)} = 26.0\textdegree$ .

For triangle DEF:

The length of segment DF is to be found,
The length of segment EF is 9,
The sine of angle E is $\sin{64\textdegree}}$ , and
The sine of angle D is $\sin{39\textdegree}$ .

Apply the law of sine:

$\displaystyle \frac{DF}{EF} = \frac{\sin{E}}{\sin{D}}$

$\displaystyle DF = \frac{\sin{E}}{\sin{D}}\cdot EF = \frac{\sin{64\textdegree}}{39\textdegree} \times 9 = 12.9$ .

7 0

2 years ago

What is the probability of rolling a 2 or not rolling a 2 using a regular 6-sided number cube?

larisa [96]

Well 100%, and 5/6 are out of the question which leaves you with 1/6 and 33.3

8 0

2 years ago

Read 2 more answers

PLEASE HELP ME!!!!! I HAVE TRIED THIS QUESTION 5X ALREADY AND I STILL CANNOT GET THE RIGHT ANSWER!!! I KNOW THE ANSWER BUT I HAV

kirill [66]

Answer:

x = 3 and y = 2

or

(3,2)

Step-by-step explanation:

first equation (LCM = 3 x 4 x 5 = 60)

(x+2)/5 - (9-x)/3 = (y - 6)/4

12(x+2) - 20(9-x) = 15(y - 6)

12x + 24 - 180 + 20x = 15y - 90

32x - 15y = -90 - 24 + 180

32x - 15y = 66

second equation:

8(x + 2) - (2x + y) = 2(x + 13)

8x + 16 - 2x - y = 2x + 26

6x - y + 16 = 2x + 26

4x - y = 10

Now you have 2 equations:

4x - y = 10 ---> y = 4x - 10

32x - 15y = 66

Substitute y = 4x - 10 into 32x - 15y = 66

32x - 15(4x - 10) = 66

32x - 60x + 150 = 66

-28x = -84

x = 3

y = 4(3) - 10

y = 12 - 10

y = 2

Solutions: x = 3 and y = 2

6 0

2 years ago

how is the formula for the area of a trapezoid related to the formula for the area of a parallelogram?

chubhunter [2.5K]

Answer:

They are related becasue if you find the area of a parallelogram then divide it by two then you have the area of a triangle

Step-by-step explanation:

3 0

3 years ago