Final answer:
Using trigonometry, the problem can be solved with the information of angles with respect to the horizontal. Since tan(45°) is 1, Yolanda's distance from the screen is equal to the height of the screen. Applying the tan(30°) relation to the information about Kim's line of sight, we deduce that Yolanda is approximately 26.0 feet away from the screen.
Step-by-step explanation:
The problem can be solved using trigonometry. To determine how far Yolanda is from the screen, we can use the tan function of the angle 45° that Yolanda's line of sight makes with the horizontal. Since tan(45°) = 1, it means that Yolanda's distance from the screen (which we will call y) is equal to the height of the screen (h).
Using Kim's angle of 30°, we can create a right triangle where the opposite side is the height of the screen (h), the adjacent side is the distance from Yolanda to the screen (y) plus 15 feet, and the angle is 30°. The tan(30°) is equal to h/(y+15). Since tan(30°) is well-known to be √3/3 (or approximately 0.5774), we can use the equation √3/3 = h/(y+15) to find the value of y.
Since we already established that y = h, we can substitute h with y in the above equation and get √3/3 = y/(y+15). Multiplying both sides of the equation by (y+15) gives us y√3/3 = y. Crossing out the y's from both sides and solving for y through algebraic manipulations gives us y = 15√3, which is approximately 25.98. Rounding to the nearest tenth gives us 26.0 feet.