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if you have a 30 60 90 triangle and the hypothesis is a what are the lengths of the triangle of the other two sides

User Hiedi
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1 Answer

12 votes
12 votes

The triangle is given with angles, 30, 60 and 90 degrees. Since only one side is given, we shall find the other two sides one after the other by applying the Trigonometry ratios.

Using the angle30 as the reference angle,

Sin 30 = Opposite/ Hypotenuse

Note that the hypotenuse (longest side) has been provided as 8, and the opposite is the side facing the reference angle. Since we have chosen 30 as the reference angle, the side facing angle 30 shall be the opposite.

Sin 30 = Opposite/8

By cross multiplying you now have,

Sin 30 * 8 = Opposite

By use of calculator, Sin 30 equals 0.5

0.5 * 8 = Opposite

4 = Opposite

Now that two of the sides have been calculated, we can further calculate the third side by either use of Pythagoras theorem or the Trigonometry ratios

The Triangle now has three angles named and two sides named as follows;

Sin 60 = Opposite/Hypotenuse

Sin 60 = Opposite/8

Sin 60 in the calculator is given as 0.8660

0.8660 * 8 = Opposite

6.928 = Opposite

Opposite is approximately 7 units

if you have a 30 60 90 triangle and the hypothesis is a what are the lengths of the-example-1
User Kristian Spangsege
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