Question

(2) $ab = 5sqrt{3}$
$ac = 10$
$bc = 5$

Explanation:

Step1: Match side to 30° angle

In the right triangle, $\angle A = 30^\circ$, and the side opposite to it is $BC=5$. From the table, this side corresponds to $x$, so $x=5$.

Step2: Fill 30° side value

The box for the 30° row is $x=5$.

Step3: Calculate 60° side value

The side opposite 60° is $AB=5\sqrt{3}$, which matches $x\sqrt{3}$. Substitute $x=5$: $5\sqrt{3}$, so the box for the 60° row is $5\sqrt{3}$.

Step4: Calculate 90° side value

The hypotenuse $AC$ is opposite 90°, which corresponds to $2x$. Substitute $x=5$: $2\times5=10$, so the box for the 90° row is $10$.

Answer:

• 30° row box: 5
• 60° row box: $5\sqrt{3}$
• 90° row box: 10