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The hypotenuse of a right triangle is 25 cm long One leg is 17 cm longer than the other Find the length of the shorter leg?
Call the length of the shorter leg s. Then, from the Pythagorean theorem,
s2 + (s + 17)2 = 252. Expanding the binomial results in:
s2 + s2 + 34s + 172 = 252, or
2s2 + 34s + 289= 625, or
s2 + 17s - 168 = 0. This can be factored into:
(s + 24)(s - 7) = 0, which is true when s = -24 or 7. Only the latter answer makes sense for a physical triangle; therefore, the shorter leg of this triangle is 7 cm long.
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How do you find the length of the sides of a right triangle when you know the hypotenuse?
If it is a 45-45-90 triangle, then divide the hypotenuse by the square root of 2. If it is a 30-60-90 triangle, then the shorter leg would be the hypotenuse divided by 2. And the longer leg would be the the shorter leg multiplied by the square root of 3.
Are true statements about a 30-60-90 triangle?
.The hypotenuse is twice as long as the shorter leg The longer leg is twice as long as the shorter leg.
What could be the ratio of the length of of the longer leg of a 30 60 90 triangle to the length of its hypotenuse?
In a 30° 60° 90° triangle, the ratio (long leg)/hypotenuse = sqrt(3)/2 ~ 0.866The ratio (short leg)/hypotenuse = 1/2 = 0.5
The ratio of the length of the longer leg of a 30-60-90 triangle to the length of its hypotenuse?
Starting with an equilateral triangle of side 2, dropping a perpendicular from one vertex to the opposite base creates two equal right angled triangles with hypotenuse of length 2, base length 1 and height of length √(22 - 12) = √3 which is the longer leg of the 30-60-90 triangle. Thus the ratio of longer_leg : hypotenuse is √3 : 2
Can a leg of a right triangle be longer than the hypotenuse?
No.
