can someone explain to me how to do these????

Question

if one leg of a right triangle measures 3 centimeters and the other leg measures 6 centimeters, what is the length of the hypotenuse?

in a right triangle, the length of hypotenuse is 20 inches and the length of one leg is 15 inches. what is the lenth of the other leg?

in a right triangle, one leg measured 4 inches and the other leg measures 6 inches. what is the lenght of the hypotenus?

Answer 1

These are all Pythagorean Theorem.

(Hypotenuse)^2 = (Leg)^2 + (Leg)^2

1)
h^2 = (3)^2 + (6)^2
h^2 = 9 + 36
h^2 = 45
h = sqrt 45
h = sqrt (9*5)
h = sqrt 9 * sqrt 5
h = 3 sqrt 5

2)
20^2 = 15^2 + x^2
400 = 225 + x^2
175 = x^2
sqrt 175 = x
sqrt (25*7) = x
sqrt 25 * sqrt 7 = x
5 sqrt 7 = x

3)
h^2 = 4^2 + 6^2
h^2 = 16 + 36
h^2 = 52
h = sqrt 52
h = sqrt (4*13)
h = sqrt 4 * sqrt 13
h = 2 sqrt 13

Answer 2

Well to solve these you can use the Pythagorean theorem, which is a squared + b squared = c squared. a and b always represent the legs in a right triangle and c represents the hypotenuse. Remember the Pythagorean theorem ONLY works in right triangles.

In your first problem a would = 3 centimeters and b would = 6 centimeters. So just solve out, 3 squared + 6 squared = c squared. 3 squared = 9 and 6 squared = 36, add them together, 45 = c squared, so now to finish the problem you take the square root of each side to cancel out the squared so your answer is square root of 45 = c.
Heres the actual problems set up:
a squared + b squared = c squared
3 squared + 6 squared = c squared
9 + 36 = c squared
45 = c squared
square root of 45 =c

In your second problem a would = 15 and c would = 20. So just solve out, 15 squared + b squared = 20 squared. 15 squared = 225 and 20 squared = 400. You now have 225 + b squared = 400. Subtract 225 from both sides, now having b squared = 175. Square root both sides to cancel out the squared, leaving b = square root of 175
Heres the actual problems set up:
a squared + b squared = c squared
15 squared + b squared = 20 squared
225 + b squared = 400
b squared = 175
b = square root of 175

In your last problem a would = 4 and b would = 6. Solve out, 4 squared + 6 squared = c squared. 4 squared = 16 and 6 squared = 36, so therefore you problem is, 52 = c squared. Square root both sides to cancel out the squared, leaving square root of 52 = c squared.
Heres the actual problems set up:
a squared + b squared = c squared
4 squared + 6 squared = c squared
16 + 36 = c squared
52 = c squared
square root of 52 = c

Answer 3

in a right triangle hyp^2 = aside^2 + otherside^2 [pythagoras]

3^2 + 6^2 = 9+36=45 = 9*5 so hyp = 3sqrt(5)

20^2-15^2 = 400 - 225 = 175 = 25*7, so other leg = 5 sqrt(7)

4^2 + 6^2 = 16 + 36 = 52 = 4*13 so hyp = 2sqrt(13)

Answer 4

Pythagoream Theorem

c² = a² + b²

√c² = ± √(3)² + (6)²

√c² = ± √9 + 36

√c² = ± √45

c = ± 6.708203933 centimeters

x = ± 6.7 centimeter rounded to one decimal place

- - - - - -

c² = a² + b²

c² - a² = b². . . Use this formula

± √c² - √a² = √b²

± √(20)² - (15)² = √b²

± √400 - 225 = √b²

± √175 = √b²

± 13.22875656 = b

- - - - - - -s-

Answer 5

a^2 + b^2 = c^2
where a & b are the short legs of the triangle.
1. 3^2 + 6^2 = c^2
9+36=c^2
c=sqrt(45)=6.708

2. a^2 + 15^2 = 20^2
a^2 + 225 = 400
a^2 = 175
a=sqrt(175)=13.23

3. 4^2 + 6^2 = c^2
16 + 36 = c^2
c=sqrt(52)=7.21

Answer 6

To answer the first statement there - To work out the length of the hypotenuse, you would firstly square the two sides given and add them together (i.e. 3{squared} + 6{squared}) and the sum of this equation (i.e.45) would be equal to the square of the hypotenuse, therefore in order to work out the hypotenuse you must square root this number {square root of 45} and you will find your answer which is roughly equal to 6.7. I hope i have explained this in an understandable way :)

Answer 7

Use Pythagoras theorem for all
Sum of Square of the two sides = Square of the hypotenuse

(one side)^2 + (other side)^2 = (hypotenuse)^2

Answer 8

Pythagoras Theorem
Asquared + Bsquared = C squared
so for part A
3squared + 6squared = Csquared
C squared = 9 + 36
C = square root of 45
C = 6.708 cm to 3 decimal places
Use this theorem for the other parts of your question

Answer 9

S?ma, D?na, Danda, Bheda is a ability of persuasion utilized by ability of Hindu Kshatriyas.those are 4 of the seven techniques utilized by ability of Kings to rule their Kingdoms. the different 3 being, Maya, Upeksha, Indrajala. it truly is a political technique to recommendations-set a given subject. initiate with conciliation or mushy persuasion (S?ma). If that doesn't help, furnish money/cloth wealth (D?na). Use punishment or violence (Danda) to ensure the region the place the previous 3 fail.If that still does not replace the status quo, use hazard or reason dissension (Bheda). Use of illusions or deceit (M?ya), intentionally ignoring people (Upeksha), use of jugglery (Indraj?l?) are additionally suggested to ensure any subject. Sama, dana, danda , bheda have been the political methodologies prescribed by ability of the scriptures. all of the 4 have been to be meditated. the 1st replaced into sama: political conciliation, humane; dana: a political sacrifice; danda : there's a combat , and if each little thing fails bheda: a hazard that something undesirable might take place if ideal steps are no longer taken to deliver some conciliation. interior the context of Mahabharata, ultimately it replaced into desperate by ability of the properly-wishers of the Pandavas that the three until eventually now approaches ought to no longer prevail, nevertheless they tried their superb interior the pursuance of those regulations. conflict befell, and info of the conflict are given interior the Bhishmaparva, the Dronaparva, and the Karnaparva of the Mahabharata, ending with the Shantiparva the place, by ability of mysterious maneuvers and divine interventions of dissimilar types, the conflict replaced into gained on the fringe of the Pandavas. the supervisor of the Pandavas, Yudhishthira, replaced into topped king.

Answer 10

I won't do your work for you, because you won't learn anything that way, but all you need is a calculator and this equation :
a squared + b squared = c squared, where a and b are the legs of the triangle, and c is the hypoteneuse. good luck.