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The image displays three mathematical problems. I will go through each one, solve them, and show the detailed solutions.

### Problem 3:
**In triangle ABC, \( A = 45^\circ \) and \( C = 70^\circ \). The side opposite angle \( C \) is 10 m. What is the side opposite angle \( A \)?**

**Solution:**
We can use the Law of Sines to solve this:
\[
\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}
\]
where \( a \), \( b \), and \( c \) are the sides opposite angles \( A \), \( B \), and \( C \) respectively.

1. First, calculate angle \( B \):
   \[
   B = 180^\circ - A - C = 180^\circ - 45^\circ - 70^\circ = 65^\circ
   \]

2. Apply the Law of Sines:
   \[
   \frac{a}{\sin(45^\circ)} = \frac{10}{\sin(70^\circ)}
   \]
   Solving for \( a \):
   \[
   a = \frac{10 \times \sin(45^\circ)}{\sin(70^\circ)}
   \]

Let's compute this:

The side opposite angle \( A \) is approximately \( 7.52 \, \text{m} \).

---

### Problem 4:
**A statue 2 meters high stands on a column that is 3 meters high. An observer in level with the top of the statue observed that the column and the statue subtend the same angle. How far is the observer from the statue?**

**Solution:**
This forms a geometric problem. The observer sees the same angle for both the 2-meter statue and the 3-meter column. Let the distance from the observer to the base of the column be \( d \).

Since the angles subtended by the statue and the column are equal, we use the fact that the ratio of their heights is the same as the ratio of the distances from the observer:
\[
\frac{3}{d} = \frac{2}{d - x}
\]
where \( x \) is the horizontal distance between the top of the column and the statue. Solving for \( d \).

I'll calculate this next.The distance \( d \) from the observer to the statue is \( 3x \), where \( x \) is the horizontal distance between the top of the column and the statue. However, without additional information about \( x \), the problem remains unsolved numerically. More context or data is needed to calculate the exact distance.

---

### Problem 5:
**Figure 6 shows a mid-air refueling scenario where military aircraft are involved. Assuming the elevation angle that the hose makes with the plane being fueled is \( \theta = 30^\circ \), what should the altitude difference \( a \) between the two planes be?**

**Solution:**
We can interpret this problem as a right triangle where the hose forms the hypotenuse, the altitude difference \( a \) is the opposite side, and the distance between the planes horizontally is the adjacent side.

Using trigonometry:
\[
\tan(\theta) = \frac{a}{\text{horizontal distance}}
\]
Rearranging:
\[
a = \text{horizontal distance} \times \tan(30^\circ)
\]

To proceed, we need the horizontal distance between the planes. Do you have that value? Otherwise, we can express the altitude difference in terms of the unknown horizontal distance.

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This page provides complete step-by-step solutions for problems involving the Law of Sines, altitude differences in military refueling, and calculating observer distance to a statue using trigonometric principles. Suitable for Grades 10-12.

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