Question

1. what is the length of u and v in this 30 - 60 - 90 triangle? a) u = 4√3 v = 8 b) u = 16 v = 8 c) u = 8 v = 4√3 d) u = 4√2 v = 8 11. find x using special triangle rules a) 10 b) 10√2 c) 10√3 d) 20

Explanation:

Step1: Recall 30 - 60 - 90 triangle rules

In a 30 - 60 - 90 triangle, if the side opposite the 30° angle is $a$, the side opposite the 60° angle is $a\sqrt{3}$ and the hypotenuse is $2a$.

Step2: Solve for question 10

The side adjacent to the 60° angle is 4. Since the side opposite the 30° angle is 4, the hypotenuse $u = 2\times4=8$ and the side opposite the 60° angle $v = 4\sqrt{3}$.

Step3: Solve for question 11

The side opposite the 30° angle is 10. The hypotenuse $x$ (opposite the 90° angle) is given by $x = 2\times10=20$ as the hypotenuse is twice the length of the side opposite the 30° angle in a 30 - 60 - 90 triangle.

Answer:

1. c) $u = 8, v = 4\sqrt{3}$
2. d) 20