6 is a leg
x is the hypotenuse
and the triangle is a 45 degree and a 90 degree triangle
2007-02-02 05:13:43 · 9 answers · asked by M 1 in Science & Mathematics ➔ Mathematics
the other leg=6
hypotenuse=sq.rt.6^2+6^2
=sq.rt.72
=6rt2
2007-02-02 05:17:53 · answer #1 · answered by raj 7 · 1⤊ 0⤋
The legs of a right triangle are the sides opposite the acute angles of the triangle and the sides adjacent the right angle of the triangle.
Since a triangle has three angles, and we know that two of the are 45 degrees and 90 degrees, we use the fact that the three angles of a triangle always equal 180 degrees. So, you say 45+90+x=180 (x being the unknown angle). Then you add 45 and 90, and get 135+x=180. Then, you subtract 135 from both sides, since what you do to one side of the equation you do to the other side of the equation, which leaves x alone. So, 180-135=45, and since you have x alone, x=45 degrees.
Now, all we have to do is use the 45-45-90 theorem for right triangles, which is: In a 45-45-90 degree triangle, the hypotenuse of the right triangle is equal to the square root of two times one of the legs.
Of course it doesn't matter which leg you multiply by the square root of two, because both are equal in this type of triangle. So your hypotenuse will be the same no matter which one you use.
Therefore, since 6 is a leg, by the 45-45-90 theorem, the hypotenuse would be 6 times the square root of two (which you'd write as 6 with the square root of two symbol right next to it). Therefore, x=6 times the square root of two. So, that's your value of x.
There you go. I'm happy I could help. :)
2007-02-02 05:42:10 · answer #2 · answered by iamanicecaringfriend 3 · 0⤊ 0⤋
It is the square root of 72. Approximately 8.485. Since it's a 45,45,90 triangle, you know the other leg is 6. Therefore the answer can be obtained via a^2+b^2=c^2 where a=6, b=6, and c=x. Solve for x.
2007-02-02 05:22:13 · answer #3 · answered by Jerm 1 · 0⤊ 0⤋
Sides are 6, 6 and x where x is the hypotenuse
cos 45° = 6 / x
x cos 45° = 6
x = 6 / cos 45° = 8.49
2007-02-02 05:21:17 · answer #4 · answered by Como 7 · 0⤊ 0⤋
sin(45)=6/x
x=6 square root 2
2007-02-02 05:18:00 · answer #5 · answered by Anonymous · 0⤊ 0⤋
It is an isosceles right triangle with equal legs which means the hypotenuse is sqrt(2) x the leg by Pythag. soooo.... x=6(sqrt(2))
2007-02-02 05:26:23 · answer #6 · answered by rhino9joe 5 · 0⤊ 0⤋
The correct answer is 6(sqrt2). Trust me.
sqrt72 is = 6(sqrt2). You just have to simplify.
2007-02-02 05:21:49 · answer #7 · answered by Anonymous · 0⤊ 0⤋
square root of 72
2007-02-02 05:18:01 · answer #8 · answered by slider 2 · 0⤊ 0⤋
x*x = 6*6 + 6*6 = 72
sqrt(72) = 8.4853 (more or less)
2007-02-02 05:21:47 · answer #9 · answered by Isme M 2 · 0⤊ 0⤋