How to find the lenghts of a triangle's legs, given the hypotenuse.?

Question

I have the following question on my math homework, and cannot find a way to fin the answer. The question is:

Compute the length of the legs a & b, of a 90-45-45 triangle, Given the hypotenuse, c=50.

If anyone knows how to set up this problem, please let me know! Thank you anyone who can help!!!!

Answer 1

Pythagorean Theorem
A = B in a 90-45-45 triangle, so:

50² = A² + B². Substitute with the above formula, so 50² = A² + A². Simplify to 50² = 2(A²). Calculate 50² for 2500, so 2500 = 2(A²). Divide both sides by 2, so 1250 = A². Find square root of 1250 = 35.3553.

Check answer: 35.3553² + 35.3553² = 50²; 1250+1250=2500

Answer 2

That's a very simple math problem.

You said that the triangle has an angle of 90-45-45.
That means that it is a right triangle with the same size of legs (a=b), coz its base angle are the same (45).

So to compute for the legs, given a hypotenuse, follow this step.

c^2 = a^2 + b^2
since a = b
c^2 = 2a^2
solving for a
a = sqrt ( (c^2) / 2)
a = sqrt ((50^2)/2)
a = sqrt (2500/2)
a = sqrt (1250)
a = sqrt (625 * 2)
a = 25 * sqrt(2)

that's the answer.

Oh by the way if encounter another probelem like this, you may compute for the legs by just dividing the given hypotenuse by two and then put sqrt(2). And then simplify. that's all

Answer 3

The hypotenuse is opposite the 90 degree angle and the other two sides have equal angles with the hypotenuse so must be equal length.

Good luck - Mike

Answer 4

i attempted quadratic equation too, in spite of the incontrovertible fact that it wont arrive at x=6, the respond for sure is x=6. i think of trial and mistake is the main suitable answer for that subject. 2x^2 + 4x - ninety six = 0 in basic terms positioned @ x=6 then subtitute to the equation, ok? 2(36) + 4 (6) - ninety six = 0 seventy two + 24 - ninety six = 0, as a result 0=0, examine! legs are base=6, top=6+2=8

Answer 5

45-45-90 is a special triangle with legs are x's and hypotenuse is x radical 2
we know that the h is 50 so we have 50=x radical 2
solve for x we have 35.35. THe legs are 35.35

Answer 6

this is an isoceles right triangle so you use the Pythagorean theorem. Let x=each leg
x^2+x^2=2500
2x^2=2500
x^2=1250
now if you don't know the square root use a calculator and find the square root of 1250. .
x=35.36, rounded to the hundredths

Answer 7

Since there are 2 equal angles, this is an isosceles triangle, so a=b.

a^2+b^2=c^2
2a^2=50^2
a^2=50^2/2
a=b=50/sqrt(2)=25sqrt(2)/2

Answer 8

a^2 + b^2 = c^2
a = b

a^2 + a^2 = 50^2
2a^2 = 2500
a^2 = 1250
a = sqrt(625 * 2)
a = 25sqrt(2)

the other 2 legs are 25sqrt(2)

this only works because you have an isosceles triangle.

Answer 9

Since the two acute angles are the same, the sides opposite them are also the same. So:
a=b
and therefore
a²+b²=c² → 2a²=c²