a large birdcage has the shape of a rectangular prism. a straight branch of length b (in meters) is placed…
a large birdcage has the shape of a rectangular prism. a straight branch of length b (in meters) is placed in the cage going from one corner to the opposite corner as shown in the figure. (the figure is not drawn to scale.) (a) find a. a = m (b) use your answer to part (a) to find b, the length of the branch. round your answer to the nearest tenth of a meter. b = m
Answer
Explanation:
Step1: Find the diagonal of the base
We use the Pythagorean theorem for the base of the rectangular - prism with sides 3m and 4m. The diagonal of the base (a) is given by (a=\sqrt{3^{2}+4^{2}}). [a = \sqrt{9 + 16}=\sqrt{25}=5]
Step2: Find the length of the branch (b)
Now, we consider a right - triangle with legs (a = 5m) and the height of the prism (h = 7m). Using the Pythagorean theorem again, (b=\sqrt{a^{2}+7^{2}}). Since (a = 5), we have (b=\sqrt{5^{2}+7^{2}}=\sqrt{25 + 49}=\sqrt{74}\approx8.6)
Answer:
(a) (a = 5) (b) (b\approx8.6)