https://file.aiquickdraw.com/mathbot/file/172923104892860i62oln.jpg

Let's analyze and solve the multiple-choice questions (MCQs) from the image.

### 1. The distance of the point (-6, 8) from the x-axis is…
The distance from the x-axis is determined by the y-coordinate of the point because the x-axis is horizontal. So, for point \((-6, 8)\), the distance is the absolute value of the y-coordinate, which is 8 units.

**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…
We can apply trigonometry here. The angle of depression is equal to the angle of elevation from the object to the top of the tower, forming a right triangle. The height of the tower is 75 m (opposite side), and the angle is 30°.

Using the formula:
\[
\tan(30^\circ) = \frac{\text{height of the tower}}{\text{distance from the object (adjacent side)}}
\]
\[
\tan(30^\circ) = \frac{75}{\text{distance}}
\]
Since \(\tan(30^\circ) = \frac{1}{\sqrt{3}}\), we have:
\[
\frac{1}{\sqrt{3}} = \frac{75}{\text{distance}}
\]
Solving for distance:
\[
\text{distance} = 75 \sqrt{3} \text{ meters}
\]

**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…
If the height of the man and the length of the shadow are equal, this forms an isosceles right triangle where the opposite and adjacent sides are equal. This corresponds to a 45° angle.

**Answer**: (a) 45°.

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Would you like more details or clarifications on any of these problems?

Here are some related questions you might explore:
1. What is the general formula for the distance between a point and an axis?
2. How can trigonometric functions be applied to solve height and distance problems?
3. How do we calculate angles of elevation and depression in real-life scenarios?
4. What is the relationship between the angle of depression and the angle of elevation?
5. How can you determine the length of a shadow using trigonometric ratios?

**Tip**: When solving height and distance problems, always sketch a diagram to visualize the relationships between the different components.

The distance of the point (-6, 8) from the x-axis, the distance of an object from a tower with an angle of depression of 30°, and the angle of elevation when the height and shadow length are equal.

Solve geometry and trigonometry problems such as finding the distance from a point to the x-axis, calculating the distance from a tower using the angle of depression, and determining the angle of elevation when height and shadow length are equal. Ideal for Grades 9-10 students.

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