Question

If angle A =90 degree , b=1 cm and a =2 cm then solve the following right angled triangle ABC ​

Answer 1

• Angle A = 90 degrees, side a = 2.
• Angle B = 30 degrees, side b = 1.
• Angle C = 60 degrees, side c =
  `√(3)`.

Side c:

• If angle A is 90 degrees, side a is the hypotenuse.
• 
  `c^(2) + b^(2) = a^(2)` <--- this is NOT the correct way to write the Pythagorean theorem. I changed it to fit the side lengths. Normally, it is
  `a^(2) + b^(2) = c^(2)`, where c is the hypotenuse. Since a is the hypotenuse, I switched the variables.
• 
  `c^(2) + (1)^(2) = (2)^(2)`
• 
  `c^(2) + 1 = 4`
• 
  `c^(2) = 3`
• 
  `c = √(3)`

Finding the angles:

• In a 30-60-90 right triangle, the...
• Shortest leg = x
• Longest leg =
  `x√(3)`
• Hypotenuse = 2x
• In this case, the shortest leg is 1, the longer leg is
  `√(3)` (or
  `1*√(3)`), and the hypotenuse is 2 (or
  `2*1`).
• As a result, this is a 30-60-90 triangle -- angle B is 30 degrees while angle C is 60 degrees.