In a right hypotenuse AC = 10 cm and ∠A = 60°, then find the length of the remaining sides.

Given: ∠A = 60^o and AC = 10cm

Now,

Now, we know that

⇒ BC = 5√3 cm

In right angled ∆ABC , we have

⇒ (AB)² + (BC)² =(AC)² [by using Pythagoras theorem]

⇒ (AB)² + (5√3)² = (10)²

⇒ (AB)² +(25×3) =100

⇒ (AB)² +75 = 100

⇒ (AB)² = 100 – 75

⇒ (AB)² = 25

⇒ AB =√25

⇒ AB = ±5

⇒ AB = 5cm [taking positive square root since, side cannot be negative]

∴ Length of the side AB = 5cm and BC =5√3 cm