Question

The length of the hypotenuse of an isosceles, right triangle is 12 6 . How many degrees are in each angle? What is the length of each leg?

Answer 1

Isosceles right triangle is a 90 45 45 degree triangle
leg = 12.6 / sq rt(2)
leg = 12.6 / 1.4142135624
leg = 8.909545443

Answer 2

Answer:

Length of each leg = 8.91 units

Length of each angle other than right angle is 45°

Step-by-step explanation:

For better understanding of the solution see the attached figure :

ΔABC is right angled isosceles triangle ⇒ AB = BC

Now, by using Pythagoras theorem :

AC² = AB² + BC²

12.6² = 2×AB²

AB² = 79.38

AB = 8.91 units

So, BC = 8.91 units

Now, Since AB = AC

⇒ ∠BAC = ∠ACB ( equal sides have equal angles opposite to them)

Now, By using angle sum property of a triangle

∠ABC + ∠BAC + ∠ACB = 180°

90° + 2∠BAC = 180°

2∠BAC = 90°

∠BAC = 45°

⇒ ∠ACB = 45°