TLM: At the basketball stadium, the stadium screen or monitor is a rectangle. If you draw a line through the centre, you get two triangles; each with a 90° angle. As a rule, the other two angles added to the 90° angle must add up to 180° degrees. Always, all three angles must add up to 180°( 180 degrees). The right angle is angle A. What is the value of angle B if angle C is 45°? There is damage to the screen. If the total area of the screen is 7m x 5 m, what is the total area that the new screen must cover? The screen is compromised of smaller pixel screens with each small screen covering 2m x 3m. How many such smaller screens would you need to complete replacement of the jumbo screen? If the basketball arena has 20,000 seats, how much does the team earn on each game if they get 30% of the ticket sales and each ticket is $40.00 per ticket?

 TLM:    At the basketball stadium, the stadium screen or  monitor is a rectangle.  If you draw a line through the centre, you get two  triangles; each with a 90° angle.  As a rule, the other two angles added to the 90° angle must add up to 180° degrees.  Always, all three angles must add up to 180°( 180 degrees).  The right angle is angle A. What is the value of angle   B if angle C is 45°? There is damage to the screen. If the total area of the screen  is 7m x 5 m, what is the total area that the new screen must cover? The screen is compromised of smaller pixel screens with each  small screen covering 2m x 3m. How many such smaller screens would you need to complete replacement of the jumbo screen?  If the basketball arena has 20,000 seats, how much does the team earn on each game if they get 30% of the ticket sales and each ticket is $40.00 per ticket? 

Here is the step-by-step breakdown and discussion of your basketball stadium calculations:

### 1. Finding the Value of Angle B

The interior angles of any triangle always add up to exactly 180^\circ. A rectangular screen split diagonally creates two right-angled triangles where:

 * **Angle A (The Right Angle):** 90^\circ

 * **Angle C:** 45^\circ

To find the remaining angle, Angle B, subtract the known angles from the total:

Angle B is **45^\circ**, which means the diagonal splits the rectangle into two isosceles right triangles.

### 2. Total Area of the New Screen

The total area that the new jumbo screen must cover is determined by multiplying its length by its width:

The new screen must cover a total area of **40\text{ square meters}**.

### 3. Number of Smaller Pixel Screens Needed

Each smaller pixel screen covers an area of 2\text{ m} \times 3\text{ m} = 6\text{ m}^2.

 * **By Pure Area Requirement:** 

   

   Since you cannot buy a fraction of a screen, you need at least **7 screens** to cover the area.

 * **By Physical Arrangement (Without Cutting Panels):**

   Interestingly, you can perfectly cover the 8\text{ m} \times 5\text{ m} screen using exactly **7 whole panels** without needing to cut any of them, by changing their orientation:

   * **Bottom Row:** Place four panels vertically (2\text{ m} wide \times 3\text{ m} high) side-by-side. This perfectly covers an area of 8\text{ m} wide by 3\text{ m} high.

   * **Top Row:** Place three panels horizontally (3\text{ m} wide \times 2\text{ m} high) side-by-side on top of the first row. This covers an area of 9\text{ m} wide by 2\text{ m} high.

   Combined, they cover a total space of 5\text{ m} high and at least 8\text{ m} wide (with 1\text{ m} overhanging on the top row). Therefore, exactly **7 smaller screens** are required to complete the replacement.

### 4. Game-Day Ticket Revenue

Assuming the arena fills its 20,000 seats for a game:

 1. **Total Ticket Sales (Gross Revenue):** 

 2. **The Team's 30% Share:** 

The team earns **\$240,000** from ticket sales on each game.