Find length of sides

Question

1. In triangle DEF, ∠E=90°, ∠D=60°, and side DE is 1 unit long. Find the length of the other two sides. Give answers to 2 decimal places where needed. (3 marks)

Answer 1

Draw a triangle sketch and then use the appropriate SPECIAL RIGHT TRIANGLE to solve.

The rule for the SPECIAL RIGHT TRIANGLE 30-60-90 is that the hypotenuse is twice the length of the short leg. The other leg is the short leg multiplied by √3.

So, since the short leg is 1 (always the side opposite the 30° angle), then the hypotenuse side DF = 2 and side EF = 1√3 or just √3. To get the decimal equivalent, use your calculator.