+839 An isosceles right triangle has legs of length 6. What is the length of the altituse drawn to the hypotenuse?
+1006 It's the altitude, right?
If I recall correctly (haven't had school for a month, Geometry in longer, so forgive me) the altitude is the line at a direct right angle from a side?
The altitude in this case would be against the hypotenuse.
SO, for this, the legs for this side are 6 and 6. This makes it a 45 - 45 - 90 triangle, which brings up something cool: we already know the length of the hypotenuse. 45 - 45 - 90 = x - x - x*squareroot(2) Therefore, the length of the hypotenuse is 6squareroot(2)
This brings another funny fact: the altitude, because it is an isoceles right triangle, perfectly splits the hypotenuse in half. In this case, the "squareroot(2)" acts as a variable (6/2=3) and does not affect the 6 or 3.
This brings up yet another sweet thing: It just made another isoceles right triangle, except instead of the legs being 6 and 6, the legs are 3squareroot(2). The altitude is one of the legs now, and thus the altitude's length is 3squareroot(2).
Oh, and Zegroes, you're probably older than me, so you have NO RIGHT.
+128475 We can use the sine to find this....
sin(45) = opp/6 where 'opp" = altitude
6sin(45) = opp = 6/√2 or 6√2/2 or 3√2
Hey, zegroes....who you calling "olds??"
+1006 It's the altitude, right?
If I recall correctly (haven't had school for a month, Geometry in longer, so forgive me) the altitude is the line at a direct right angle from a side?
The altitude in this case would be against the hypotenuse.
SO, for this, the legs for this side are 6 and 6. This makes it a 45 - 45 - 90 triangle, which brings up something cool: we already know the length of the hypotenuse. 45 - 45 - 90 = x - x - x*squareroot(2) Therefore, the length of the hypotenuse is 6squareroot(2)
This brings another funny fact: the altitude, because it is an isoceles right triangle, perfectly splits the hypotenuse in half. In this case, the "squareroot(2)" acts as a variable (6/2=3) and does not affect the 6 or 3.
This brings up yet another sweet thing: It just made another isoceles right triangle, except instead of the legs being 6 and 6, the legs are 3squareroot(2). The altitude is one of the legs now, and thus the altitude's length is 3squareroot(2).
Oh, and Zegroes, you're probably older than me, so you have NO RIGHT.
