11 ft
Using the properties of a right triangle, we can see that ∡C is 45° as well since the sum of the angles in a triangle is 180°.
Since ∡C is 45°, we have a 45-45-90 triangle. In a 45-45-90 triangle, the hypotenuse (BC) is √2 times the length of the legs.
Given that the length of the legs are equal, if we call x the length of the legs, then BC = x√2.
Since ∡B = 45°, we can apply the Pythagorean theorem:
x^2 + x^2 = BC^2
2x^2 = BC^2
Since BC = x√2, we can substitute:
2x^2 = (x√2)^2
2x^2 = 2x^2
x = 11
Therefore, the length of BC is 11 ft.
In ΔABC, ∡A is a right angle, and m∡B = 45°.
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
1 answer