Question

In a right angled triangle. If the lengths of two of its sides are 12 cm and 5 cm, what is the length of its third side? ​

Answer 1

Step-by-step explanation:

If it’s a right triangle, and those are the legs, the hypotenuse is 13. 5-12-13 is one of the Pythagorean triples, a special set of right triangles.

If you can learn to recognize Pythagorean triples on sight, it’ll save you a lot of hassle trying to figure them out. The other common one is 3–4–5. There are lots more but the numbers get really big fast. Some problems you don’t even realize it’s a Pythagorean triple until you do all the math and all 3 sides come out as nice whole numbers.

If the hypotenuse is 12 and one of the legs is 5, the other leg is sqrt(119). (Don’t know how to make a square root symbol here.)

(12^2) - (25) = (other side)^2

144–25 = 119

Other side = sqrt(119)

If it’s not a right triangle and you know the interior angles, use law of sines or cosines.

Law of sines: (sin(Angle A))/(side across from A, aka lowercase a) = (sin(Angle B))/ (b) = (sin(Angle C))/(c)

If two angles are given the third one is really easy to find. Add up the other two angles and subtract that number from 180.

Answer 2

In a right angled triangle. If the lengths of two of its sides are 12 cm and 5 cm, what is the length of its third side?

ANSWER:

$\large\underline\blue(\bold{Formula\:used}$:Pythagoras theorem

= a²+ b²= c²

= 12²+ 5⁵= c²

= 12 × 12+ 5 × 5 = c²

= 144× 25= C²

= 169 = C²

= √13 = C

A = 12 , B = 5 , C = 13