Asked by Jyar
Two sides of a right triangle measure 10 m and 8 m. Explain why this is not enough information to be sure of the length of the third side. Give two possible values for the length of the third side.
Answers
Answered by
mathhelper
You said it was a right triangle, assuming you meant
right-angled triangle.
You are given 2 sides, but did not state which two sides.
Clearly the hypotenuse has to be the longest side.
case 1: 10 m is the hypotenuse, then
a^2 + 8^2 = 10^2
a^2 = 100-64 = 36
a = 6, the 3 sides are 6, 8, and 10 (multiples of the standard 3-4-5 right-angled triangle)
case 2. the two given sides are the sides containing the 90° angle
c^2 = 10^2 + 8^2 = 164
c = √164 = 2√41 , the 3 sides are 8, 10 and 2√41
right-angled triangle.
You are given 2 sides, but did not state which two sides.
Clearly the hypotenuse has to be the longest side.
case 1: 10 m is the hypotenuse, then
a^2 + 8^2 = 10^2
a^2 = 100-64 = 36
a = 6, the 3 sides are 6, 8, and 10 (multiples of the standard 3-4-5 right-angled triangle)
case 2. the two given sides are the sides containing the 90° angle
c^2 = 10^2 + 8^2 = 164
c = √164 = 2√41 , the 3 sides are 8, 10 and 2√41
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