https://file.aiquickdraw.com/mathbot/file/1726102093747tlpgbv0d.jpg

This image contains the solution to a trigonometric problem involving two parts (a and b).

### Breakdown of the solution:

#### a) 
1. **Finding PR using Pythagoras' theorem:**
   \[
   PR^2 = 2400^2 + 350^2 = 5882500
   \]
   \[
   PR = \sqrt{5882500} = 2425.39 \, \text{m} \quad (\text{rounded to } 2425 \, \text{m})
   \]

2. **Finding \( \angle PRQ \) using the tangent ratio:**
   \[
   \tan \angle PRQ = \frac{2400}{350}
   \]
   \[
   \angle PRQ = \tan^{-1}\left( \frac{2400}{350} \right) \approx 81.70^\circ \quad (\text{rounded to } 82^\circ)
   \]

#### b)
1. **Finding \( \angle RSP \):**
   \[
   \angle RSP = 82^\circ - 3^\circ = 79^\circ
   \]

2. **Using the sine rule to find SR:**
   \[
   \frac{SR}{\sin 3^\circ} = \frac{2425}{\sin 79^\circ}
   \]
   \[
   SR = \frac{2425 \times \sin 3^\circ}{\sin 79^\circ} \approx 129.44 \, \text{m} \quad (\text{rounded to } 129 \, \text{m})
   \]

Would you like further details or clarifications on any part of this problem?

### 5 related questions:
1. What are the properties of the tangent function in a right triangle?
2. How do you calculate the sine of an angle in trigonometry?
3. What are the main steps involved in using the sine rule?
4. Why is it important to round answers in practical applications?
5. How would the answer change if the values for the triangle sides were different?

### Tip:
Always check whether the angle is acute or obtuse before using inverse trigonometric functions to avoid errors in direction.

Trigonometric problem involving Pythagoras' theorem and the sine rule to calculate side lengths and angles in a triangle.

Solve a trigonometric problem using Pythagoras' theorem and the sine rule. Calculate the side length of PR (2,425 m) and the angles (82° and 79°) in a triangle, using tangent and sine functions. Suitable for Grades 10-12.

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