https://file.aiquickdraw.com/mathbot/file/1725547753456b0hjm7dd.jpg

It looks like you've uploaded a photo containing a geometry problem related to triangle PGB. I will extract the details and solve the problem for you.

The problem states:
- **PG = 10.2 cm**
- **GB = 7.3 cm**
- **Angle HGB = 35°**

Tasks:
a) Given that angle GHB is a right angle, calculate the area of triangle PGB.

Let me now proceed to solve this.

### Step 1: Identifying key information and the formula for area
The area of a triangle can be calculated using the formula:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
In this case, the base could be either side of the triangle (PG or GB). However, we'll need to use trigonometry to find the height, using angle HGB and side GB to derive the perpendicular height from point P.

We can use the sine formula:
\[
\text{height} = GB \times \sin(\text{angle HGB})
\]

### Step 2: Calculation of the height
Let me compute this height and the area using these relations.The height of triangle PGB, calculated using the sine of angle HGB, is approximately **4.19 cm**. 

Using this height, the area of triangle PGB is approximately **21.35 cm²**.

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Would you like further clarification or details on the solution?

Here are 5 related questions to expand your understanding:
1. How would the area change if angle HGB were different?
2. How do we use trigonometric functions like sine to calculate heights in triangles?
3. What happens if PG is used as the base instead of GB? Would the height formula change?
4. How do you calculate angles in non-right triangles?
5. How does the cosine rule apply to finding unknown sides in triangles?

**Tip:** Always ensure you use the correct angle when applying trigonometric ratios to avoid errors in calculations.

Given triangle PGB where PG = 10.2 cm, GB = 7.3 cm, and angle HGB = 35°, calculate the area of triangle PGB. Assume angle GHB is a right angle.

Learn how to calculate the area of triangle PGB with sides PG = 10.2 cm, GB = 7.3 cm, and angle HGB = 35°. This problem involves using the sine function to determine the height and applying the formula for the area of a triangle. Suitable for students in Grades 9-11.

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