A man is five times as old as his son. If the son's age is y, then the man's current age is 5y. In four years' time, the product of their ages will be 340. Set up the equation for the product of their

The final answer is $\boxed{\text{D. } 5y^2 + 24y - 324 = 0}$.

Find a common denominator, which is $ab$.

Find a common denominator, which is $ab$.

To divide fractions, multiply the numerator by the reciprocal of the denominator.

The final answer is $\boxed{\text{D. } \frac{a^2 - b^2}{b^2 - ac}}$.

Since $\triangle XYZ$ is equilateral, all sides are equal ($XY = YZ = ZX = 6 \text{ cm}$) and all angles are $60^\circ$ ($\angle X = \angle Y = \angle Z = 60^\circ$).

$T$ is the midpoint of $XY$, so $XT = \frac{1}{2} XY = \frac{1}{2}(6 \text{ cm}) = 3 \text{ cm}$.

In an equilateral triangle, the line segment from a vertex to the midpoint of the opposite side is also an altitude (perpendicular to the side) and an angle bisector.
Therefore, $ZT \perp XY$, which means $\triangle XZT$ is a right-angled triangle with the right angle at $T$.
Also, $ZT$ bisects $\angle XZY$, so $\angle XZT = \frac{1}{2} \angle XZY = \frac{1}{2}(60^\circ) = 30^\circ$.

Since $\angle XZT = 30^\circ$, we need to find $\tan(30^\circ)$.

This can also be rationalized as $\frac{\sqrt{3}}{3}$.

Alternatively, using side lengths in $\triangle XZT$:
We have $XZ = 6 \text{ cm}$ (hypotenuse) and $XT = 3 \text{ cm}$ (opposite side to $\angle XZT$).
We need to find the length of $ZT$ (adjacent side to $\angle XZT$) using the Pythagorean theorem:

Now, calculate $\tan(\angle XZT)$:

The final answer is $\boxed{\text{A. } \frac{1}{\sqrt{3}}}$.

The horizontal distance between the fence and the tree is the adjacent side: $10 \text{ m}$.
The vertical height difference from the top of the fence to the top of the tree is the opposite side.

Using a calculator:

Rounding to two decimal places, $\theta \approx 53.68^\circ$.

The closest option is $53.67^\circ$.

The final answer is $\boxed{B. 53.6