a gift box has the shape of a right triangular prism. a piece of tape of length b (in inches) is placed from…
a gift box has the shape of a right triangular prism. a piece of tape of length b (in inches) is placed from one corner to the opposite corner, as shown in the figure. (the figure is not drawn to scale.) (a) find a. a = in (b) use your answer to part (a) to find b, the length of the tape. round your answer to the nearest tenth of an inch. b = in
Answer
Explanation:
Step1: Find (a) using Pythagorean theorem
In the base - right triangle with sides 3 in and 4 in, by the Pythagorean theorem (a=\sqrt{3^{2}+4^{2}}). [a = \sqrt{9 + 16}=\sqrt{25}=5]
Step2: Find (b) using Pythagorean theorem again
Now, consider the right - triangle with sides (a = 5) in and 6 in. By the Pythagorean theorem (b=\sqrt{a^{2}+6^{2}}). Substitute (a = 5) into the formula: (b=\sqrt{5^{2}+6^{2}}=\sqrt{25 + 36}=\sqrt{61}\approx 7.8)
Answer:
a = 5 in b = 7.8 in