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

1.00 and 1.73

Explanation:

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

`sin (30^(0))=(c)/(2)\Rightarrow (1)/(2)=(c)/(2)\Rightarrow 2*(1)/(2)=2*(c)/(2)\Rightarrow c=1\\sin(60^0)=(b)/(2)\Rightarrow (√(3))/(2)=(b)/(2)\Rightarrow b=√(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=√(3) b\approx 1.73`

Sides

a hypotenuse: 2.00

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b leg: 1.73

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c leg: 1.00

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