Question

Consider a triangle with angles 30o-60o-90o, with hypotenuse of length 2. Calculate the lengths of the other 2 sides and store the two calculated lengths as well as the given length in a list called sides. Use indexing to display the lengths of each of the sides in a print statement. Make sure the lengths have 2 decimal places!

Answer 1

Answer:

1.00 and 1.73

Step-by-step explanation:

1) Calculating the 1st and the 2nd leg using trigonometric function sine:

$sin (30^{0})=\frac{c}{2}\Rightarrow \frac{1}{2}=\frac{c}{2}\Rightarrow 2*\frac{1}{2}=2*\frac{c}{2}\Rightarrow c=1\\sin(60^0)=\frac{b}{2}\Rightarrow \frac{\sqrt{3}}{2}=\frac{b}{2}\Rightarrow b=\sqrt{3}\Rightarrow\: b\approx \:1.73$

Once one leg is found there is another way to find the other leg, using Pythagorean Theorem too.

$a^{2}=b^{2}+c^{2}\Rightarrow 2^{2}=b^{2}+1^{2}\Rightarrow 4-1=b^{2}\Rightarrow b=\sqrt{3} b\approx 1.73$

Sides

a hypotenuse: 2.00

-------------------------------

b leg: 1.73

--------------------------------

c leg: 1.00

--------------------------------