A right triangle has a hypotenuse of length 30 and a leg of length 10. To the nearest tenth, what is the length of the other leg?
We have the right angle triangle with sides:
The hypotenuse (h) = 30
One of the sides ( L) = 10
Find the other sides.
Let the other side be B:
Then we know that in a right angle triangle , the hypotenuse equals the square root of the sum of the sides squares:
==> hypotenuse^2 = side1^2 + side2^2
==> h^2 = L^2 + B^2
==> B^2 = h^2 - L^2
==> B = sqrt( h^2 - L^2)
= sqrt( 30^2 - 10^2)
= sqrt( 900 - 100)
= 20sqrt2 *
Then, the length of the other sides is:
B = 20sqrt2 = 28.3 ( to the nearest 10th)
In a right angled triangle ABC, if B is the right angle, then Ac is the hypotenuse.
So by Pythagoras theorem, AB^2+BC^2 = AC ^2....(1)
Given AB = 10 and the hpotenuse AC = 30.
Therefore substituting the above values in eq(1), we get:
10^2+BC^2 = 30^2.
BC ^2= 30^2-10^2 = 900-100 = 800.
BC = sqrt(800) = sqrt(400*2) = 20 sqrt2.
BC = 20*1.4142 = 28.28 nearly
BC = 28.3 near to 10th place.