Barunsangha
New Member
- Joined
- Nov 19, 2021
- Messages
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- Male
- HSC
- 2022
Question 10
A big screen is to be constructed behind the stage to display the artists during the concert and each audience member must be able to view the screen. The dimensions of the screen are 5m by 3m.
The audience for the concert is to be arranged into a seating section and a standing section. The seating section will be closest to the stage and extends the sector formed by the stage. The standing section is located behind the seating section and extends another 20 meters beyond the seating section.
Consider an audience member towards the back of the seated section and another towards the back of the standing section.
If the angle of elevation to the bottom of the screen for each seated audience member is less than 15°, their view is distorted by the audience members in front.
Similarly, if the angle of elevation for the standing audience members is less than 8°, their view is distorted by the audience members in front.
You may assume that the eye level of a seated audience member is 1.4 meters and a standing member is 1.7 meters. Draw a diagram showing all the information given above.
a) Upload the diagram in the box ( 2 marks)
b) Use your knowledge of trigonometry to determine the length of the seated section (x) and the height (h) at which the bottom of the screen must be above the ground to allow for the above conditions. Justify your answer with supporting mathematics. ( 2 marks)
A big screen is to be constructed behind the stage to display the artists during the concert and each audience member must be able to view the screen. The dimensions of the screen are 5m by 3m.
The audience for the concert is to be arranged into a seating section and a standing section. The seating section will be closest to the stage and extends the sector formed by the stage. The standing section is located behind the seating section and extends another 20 meters beyond the seating section.
Consider an audience member towards the back of the seated section and another towards the back of the standing section.
If the angle of elevation to the bottom of the screen for each seated audience member is less than 15°, their view is distorted by the audience members in front.
Similarly, if the angle of elevation for the standing audience members is less than 8°, their view is distorted by the audience members in front.
You may assume that the eye level of a seated audience member is 1.4 meters and a standing member is 1.7 meters. Draw a diagram showing all the information given above.
a) Upload the diagram in the box ( 2 marks)
b) Use your knowledge of trigonometry to determine the length of the seated section (x) and the height (h) at which the bottom of the screen must be above the ground to allow for the above conditions. Justify your answer with supporting mathematics. ( 2 marks)
