Question

The size of a TV is measured by its diagonal. You want to buy a TV that has a 32-inch screen and a height of 15.7 inches. What is the width of the TV?

Answer 1

Think of the space created with the diagonal line like a triangle. There are three sides. the longest side, the diagonal line is 32 inches. one of the other sides is 15.7 inches. Using Pythagoras theorem, we know that a^2 + b^2 = c^2, where c is the longest side of the triangle (32inches) and either a or b is 15.7inches. let's say that a is 15.7 inches. if we substitute these values we just assigned to a and c into Pythagoras' theorem above, we get 15.7^2 +b^2 = 32^2. we can simplify this to 246.49 + b^2 = 1024. We then subtract 246.49 from both sides of the equation to get b^2 = 777.51. we then square root both sides of the equation to get b = 27.88 (rounded to 2 decimal places). because b is the width of the TV, the width of the TV is 27.88 inches.
${a}^{2} + {b}^{2} = {c}^{2} \\ {15.7}^{2} + {b}^{2} = {32}^{2} \\ 246.49 + {b}^{2} = 1024 \\ {b}^{2} = 777.51 \\ b = \sqrt{777.51} \\ b = 27.88$

Answer 2

the answer to this question is 27.88