https://file.aiquickdraw.com/mathbot/file/1729230757086t7w7zlsb.jpg

Let's go through each question and solve them one by one.

---

### 1. The distance of the point (-6, 8) from the x-axis is:
The distance from the x-axis for any point \((x, y)\) is given by the absolute value of its y-coordinate.

For the point (-6, 8), the distance from the x-axis is:
\[
\text{Distance} = |y| = |8| = 8 \text{ units}
\]
**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:
In this case, we can use basic trigonometry. The angle of depression is equal to the angle of elevation from the object to the top of the tower. We know that:

\[
\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}
\]
Here, \(\theta = 30^\circ\), the height of the tower (opposite side) is 75 m, and the adjacent side is the distance we want to find (let's call it \(d\)).

\[
\tan(30^\circ) = \frac{75}{d}
\]
\[
\frac{1}{\sqrt{3}} = \frac{75}{d}
\]
\[
d = 75 \sqrt{3} \, \text{m}
\]
**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 length of the shadow are equal, we can infer that the opposite and adjacent sides of the right-angled triangle formed by the man, his shadow, and the line of sight to the sun are equal.

In such a case, the angle of elevation is 45°, because:
\[
\tan(45^\circ) = 1
\]
**Answer: (a) 45°**

---

Would you like more details on any of these solutions? Here are some related questions for practice:

1. What is the distance from the point (4, -9) to the x-axis?
2. If the height of the tower is doubled, how would the distance to the object change?
3. What is the angle of elevation when the shadow length is twice the height?
4. How would you calculate the distance from a point to the y-axis?
5. What trigonometric function would you use for an angle of depression of 60°?

**Tip**: When solving angle of depression/elevation problems, always visualize or draw the triangle to identify opposite, adjacent, and hypotenuse sides correctly.

1. The distance of the point (-6, 8) from the x-axis is... 2. If the angle of depression of an object from a 75m 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....

This problem set involves calculating the distance from a point to the x-axis, solving angle of depression problems, and determining the angle of elevation when the height and shadow of a man are equal. Perfect for Grades 9-10, with detailed solutions covering geometry and trigonometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation