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?
2 answers:
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°
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