Question

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

Answer 1

Answer:

• Angle A = 90 degrees, side a = 2.
• Angle B = 30 degrees, side b = 1.
• Angle C = 60 degrees, side c = $\sqrt{3}$.

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.
• $c^{2} + (1)^{2} = (2)^{2}$
• $c^{2} + 1 = 4$
• $c^{2} = 3$
• $c = \sqrt{3}$

Finding the angles:

• In a 30-60-90 right triangle, the...
• Shortest leg = x
• Longest leg = $x\sqrt{3}$
• Hypotenuse = 2x
• In this case, the shortest leg is 1, the longer leg is $\sqrt{3}$ (or $1*\sqrt{3}$), 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.