Use the Sine Rule.

The Sine Rule states that for a triangle with sides $a, b, c$ and opposite angles $A, B, C$:

We know that $\sin 30^\circ = 0.5$ and $\sin 60^\circ = \frac{\sqrt{3}}{2} \approx 0.866$.

The calculated value $17.32 \text{ cm}$ is closest to option B.

The final answer is $\boxed{\text{B. } 17.3 \text{ cm}}$.

38. Which formula is the cosine rule?

The Cosine Rule relates the lengths of the sides of a triangle to the cosine of one of its angles. For a triangle with sides $a, b, c$ and angle $A$ opposite side $a$, the formula is:

Comparing this with the given options:
A. $a^2 = b^2 + c^2$ is the Pythagorean theorem.
B. $a^2 = b^2 + c^2 - 2bc \cos A$ is the Cosine Rule.
C. $a/\sin A = b/\sin B$ is the Sine Rule.
D. $\tan A = \text{opposite}/\text{adjacent}$ is a trigonometric ratio for right-angled triangles.

The final answer is $\boxed{\text{B. } a^2 = b^2 + c^2 - 2bc \cos A}$.

39. A ladder $5 \text{ m}$ long leans against a wall, forming a $60^\circ$ angle with the ground. What is the height the ladder reaches on the wall?

The ladder is the hypotenuse ($H = 5 \text{ m}$).
The angle with the ground is $\theta = 60^\circ$.
The height the ladder reaches on the wall is the side opposite to the angle ($\text{Opposite} = h$).

The sine function relates the opposite side, hypotenuse, and angle:

We know that $\sin 60^\circ = \frac{\sqrt{3}}{2} \approx 0.866$.

The calculated value $4.33 \text{ m}$ is closest to option C.

The final answer is $\boxed{\text{C. } 4.3 \text{ m}}$.

40. A man sees the top of a building, an angle of elevation of $30^\circ$. He is standing $20 \text{ m}$ from the foot of the building. What is the height of the building?

The distance from the building is the adjacent side ($\text{Adjacent} = 20 \text{ m}$).
The angle of elevation is $\theta = 30^\circ$.
The height of the building is the side opposite to the angle ($\text{Opposite} = h$).

The tangent function relates the opposite side, adjacent side, and angle:

We know that $\tan 30^\circ = \frac{1}{\sqrt{3}} \approx 0.577$.

The calculated value $11.54 \text{ m}$ is closest to option C.

The final answer is $\boxed{\text{C. } 11.5 \text{ m}}$.