Question

In any right triangle, a and b are the legs, and c is the hypotenuse. Given triangle CAT,find (CA)2+(AT)2.

a) a2-2
b) C_2+a2
c) C_2-a2
d) a2+b2

Answer 1

According to the Pythagorean theorem, the sum (CA)² + (AT)² in a right triangle equals a² + b², hence the correct answer is option (d) a² + b².

Step-by-step explanation:

The question is asking to find the sum of the squares of the legs of a right triangle, where a and b are the lengths of the legs, and c is the length of the hypotenuse. According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the legs (a and b). The theorem can be written as a² + b² = c². Therefore, the sum of the squares of the legs (CA and AT) is equal to a² + b², which matches option (d).