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Let's solve the multiple-choice questions one by one:

### 1. **The distance of the point (-6, 8) from the x-axis is:**

The distance of a point \((x, y)\) from the x-axis is simply the absolute value of its \(y\)-coordinate. So, for \((-6, 8)\), the distance from the x-axis is:
\[
|y| = |8| = 8 \text{ units}
\]
**Correct Answer:** (c) 8 units

---

### 2. **If the angle of depression of an object from a 75 m high tower is 30°, then the distance of the object from the tower is:**

This forms a right triangle where:
- The height of the tower is the opposite side (75 m),
- The angle of depression is \(30^\circ\),
- We need to find the distance from the object, which is the adjacent side.

Using the trigonometric relation:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \quad \Rightarrow \quad \tan(30^\circ) = \frac{75}{\text{adjacent}}
\]
We know \(\tan(30^\circ) = \frac{1}{\sqrt{3}}\), so:
\[
\frac{1}{\sqrt{3}} = \frac{75}{\text{adjacent}} \quad \Rightarrow \quad \text{adjacent} = 75 \sqrt{3} \text{ m}
\]
**Correct Answer:** (c) 75√3 m

---

### 3. **If the height and length of the shadow of a man are equal, then the angle of elevation of the sun is:**

When the height and the shadow's length are equal, it forms a 45° angle. This is because in such a scenario, the opposite and adjacent sides of the right triangle are equal, and:
\[
\tan(\theta) = 1 \quad \Rightarrow \quad \theta = 45^\circ
\]
**Correct Answer:** (a) 45°

---

Would you like more details on any of these solutions, or have any further questions?

Here are 5 questions to think about next:
1. How do we calculate the distance of a point from the y-axis?
2. What is the difference between angle of elevation and angle of depression?
3. How can we use other trigonometric ratios to find missing sides or angles?
4. What is the relationship between the tangent function and right triangles?
5. How do real-life applications of angle of depression or elevation work?

**Tip:** For angle problems in trigonometry, always draw a sketch of the scenario to visualize the relationships!

1. The distance of the point (-6, 8) from x-axis is... 2. If the angle of depression of an object from a 75 m high tower is 30°, then the distance of the object from the tower is... 3. If the height and length of the shadow of a man are equal, then the angle of elevation of the sun is...

Solve MCQs on coordinate geometry and trigonometry. Learn how to find the distance of a point from the x-axis, calculate the distance of an object using the angle of depression, and determine the angle of elevation when the height and shadow length are equal. Suitable for Grades 8-10.

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