Problem
$10: 30$ .ull $尺 6$ Sparx Charlie Pea... MENU Bookwork code: D21 Use the information below to work out the closest distance that a cinema can put seats to the screen. Give your answer to $1 \mathrm{~d} . p$. Safety rules say that the angle of elevation from a customer's eyes to the top of the screen must be no more than $31^{\circ}$. The top of the cinema screen is $7.9 \mathrm{~m}$ above the floor. Customers' eyes are $1.2 \mathrm{~m}$ above the floor when they are sat on a seat. Back Watch video Answer $>$ $\mathrm{A} A$ sparxmaths.uk C $\uparrow$
Solution
Step 1 ：Given the angle of elevation $31^\circ$, the height of the screen $7.9 \mathrm{~m}$, and the height of a customer's eyes when seated $1.2 \mathrm{~m}$.
Step 2 ：Calculate the height difference between the screen and the customer's eyes: $7.9 - 1.2 = 6.7 \mathrm{~m}$.
Step 3 ：Use the tangent function to find the distance: $\tan(31^\circ) = \frac{6.7}{x}$.
Step 4 ：Solve for x: $x = \frac{6.7}{\tan(31^\circ)} \approx 11.2 \mathrm{~m}$.
Step 5 ：\(\boxed{11.2}\) meters is the closest distance that a cinema can put seats to the screen.
