Question

tommy is constructing a roof for a tree - house. he decides to use 45 - 45 - 90 triangles with legs that are 8 feet in length to create the roofs frame. if the hypotenuse is the width of the house, which answers represent its length? select all that apply. 16 ft. $sqrt{8^{2}+8^{2}}$ ft. $8sqrt{3}$ ft. $8sqrt{2}$ ft. 11.31 ft.

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c=\sqrt{a^{2}+b^{2}}\). In a \(45 - 45-90\) triangle, \(a = b = 8\) feet.

Step2: Calculate the hypotenuse

Substitute \(a = 8\) and \(b = 8\) into the Pythagorean theorem: \(c=\sqrt{8^{2}+8^{2}}=\sqrt{64 + 64}=\sqrt{128}=8\sqrt{2}\approx8\times1.414 = 11.31\) feet.

Answer:

B. \(\sqrt{8^{2}+8^{2}}\text{ ft}\), D. \(8\sqrt{2}\text{ ft}\), E. \(11.31\text{ ft}\)