Final answer:
To find the height of a 42-inch television with a 4:3 aspect ratio, we calculate using the diagonal and aspect ratio proportions. The calculated height comes out to be approximately 31.5 inches to the nearest tenth.
Step-by-step explanation:
The student has asked for the height of a 42-inch television screen with an aspect ratio of 4:3. To find the height, we can use the relationship between the aspect ratio and the screen size. The diagonal size, which is 42 inches, is part of a right triangle where the other two sides represent the width and height of the screen.
With the aspect ratio of 4:3, we can set up two ratios representing the width (W) and height (H) of the screen:
- Width (W)=scale/actual=4/1
- Height (H)=scale/actual=3/1
Setting up a proportion, we have:
4/3 = W/H
Given that the diagonal (D) is 42 inches, using the Pythagorean theorem, we can write:
D^2 = W^2 + H^2
42^2 = (4x)^2 + (3x)^2
After calculating, we find that x ≈ 10.5, so the height, H, is 3x ≈ 31.5 inches.
To the nearest tenth, the height of the screen is 31.5 inches.