In ΔABC, ∡A is a right angle, and m∡B = 45°.
Height is 11
right triangle
What is the length of BC? If the answer is not an integer, leave it in simplest radical form. The diagram is not drawn to scale.
(1 point)
Responses
11 ft
11 ft
11 square root 2 ft
Image with alt text: 11 square root 2 ft
11 square root 3 ft
Image with alt text: 11 square root 3 ft
22 ft
11 square root 2 ft
Using the given information, we can see that we have a right triangle where the height (opposite side) is 11 and the angle ∡B is 45° (which means it's a 45-45-90 triangle). In a 45-45-90 triangle, the sides are in the ratio 1:1:√2.
Since the height is opposite the 45° angle, it corresponds to the shorter leg of the triangle. So, the length of BC (the hypotenuse) would be 11√2. Therefore, the answer is 11 square root 2 ft.