Activity 5. Angle of Inclination. 22 January $$ 20 z 5 $$ 1. Determine the indination of the line. Round your answer to 2 decimal places with points $$ A\left(3 ; \frac{7}{2} ight) $$ $$ B(-8 ;-2) $$. 2. Determine the angle of inclination (correct to 1 decimal place) of the straight line through $$ (2 ; 1)
eq(-3 ;- $$ 3. Find the angle $$ heta $$ and round off your answer to $$ z $$ decimal places if appropriate.

Question

Activity 5. Angle of Inclination. 22 January $$ 20 z 5 $$ 1. Determine the indination of the line. Round your answer to 2 decimal places with points $$ A\left(3 ; \frac{7}{2}ight) $$ $$ B(-8 ;-2) $$. 2. Determine the angle of inclination (correct to 1 decimal place) of the straight line through $$ (2 ; 1) 
eq(-3 ;- $$ 3. Find the angle $$ 	heta $$ and round off your answer to $$ z $$ decimal places if appropriate.

UpStudy AI · Accepted Answer

Sure, let's address each part of your problem step by step.

### **1. Determine the Inclination of the Line Through Points $$ A(3, \frac{7}{2}) $$ and $$ B(-8, -2) $$**

**Step 1: Calculate the Slope ($$ m $$) of the Line**

The slope of a line passing through two points $$ A(x_1, y_1) $$ and $$ B(x_2, y_2) $$ is given by:

$$
m = \frac{y_2 - y_1}{x_2 - x_1}
$$

Plugging in the coordinates:

$$
m = \frac{-2 - \frac{7}{2}}{-8 - 3} = \frac{-\frac{11}{2}}{-11} = \frac{11}{2 \times 11} = \frac{1}{2}
$$

**Step 2: Determine the Angle of Inclination ($$ \alpha $$)**

The angle of inclination is the angle the line makes with the positive $$ x $$-axis, calculated using the arctangent of the slope:

$$
\alpha = \arctan(m) = \arctan\left(\frac{1}{2}\right)
$$

Using a calculator:

$$
\alpha \approx 26.565^\circ
$$

**Step 3: Round the Angle**

Rounded to two decimal places:

$$
\alpha \approx 26.57^\circ
$$

**Answer:** The inclination of the line is **26.57 degrees**.

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### **2. Determine the Angle of Inclination of the Straight Line Through $$ (2, 1) $$ and $$ (-3, \, \text{?}) $$**

It seems there might be a typo or missing information in this part of the question. Specifically, the coordinates for the second point are incomplete: $$ (-3, - ) $$.

**To proceed, please provide the complete coordinates of the second point.**

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### **3. Find the Angle $$ \theta $$ and Round Off Appropriately**

This part also appears to be incomplete or missing specific details required to solve the problem, such as:

- The points defining the line or additional information about $$ \theta $$.
- The value of $$ z $$ indicating to how many decimal places to round the answer.

**Please provide the missing details so I can assist you effectively.**

---

Feel free to provide the additional information, and I'll be happy to help you with the remaining parts of your problem!
**1. Inclination of the Line:** - Slope ($$ m $$) = $$ \frac{1}{2} $$ - Angle of Inclination ($$ \alpha $$) ≈ **26.57 degrees** **2. Angle of Inclination for the Line Through $$ (2, 1) $$ and $$ (-3, \, \text{?}) $$:** - **Incomplete Information:** Please provide the complete coordinates of the second point to determine the angle. **3. Angle $$ \theta $$:** - **Incomplete Information:** Please provide the necessary details to find and round the angle $$ \theta $$. **Note:** Ensure all required information is provided for accurate calculations.

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