Question

1. $a = 40, c = 58$\
2. $b = 56, c = 65$\
3. $a = 13, b = 84$\
4. $a = 16, b = 63$

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, $a^2 + b^2 = c^2$, where $c$ is the hypotenuse (longest side).

Step2: Solve Q14: Find $b$

Substitute $a=40, c=58$:
$b^2 = c^2 - a^2 = 58^2 - 40^2 = 3364 - 1600 = 1764$
$b = \sqrt{1764} = 42$

Step3: Solve Q15: Find $a$

Substitute $b=56, c=65$:
$a^2 = c^2 - b^2 = 65^2 - 56^2 = 4225 - 3136 = 1089$
$a = \sqrt{1089} = 33$

Step4: Solve Q17: Find $c$

Substitute $a=13, b=84$:
$c^2 = a^2 + b^2 = 13^2 + 84^2 = 169 + 7056 = 7225$
$c = \sqrt{7225} = 85$

Step5: Solve Q18: Find $c$

Substitute $a=16, b=63$:
$c^2 = a^2 + b^2 = 16^2 + 63^2 = 256 + 3969 = 4225$
$c = \sqrt{4225} = 65$

Answer:

1. $b=42$
2. $a=33$
3. $c=85$
4. $c=65$