Question

In ΔABC, ∡A is a right angle, and m∡B = 45°. 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.

Answer 1

[AI-generated answer — Bot GPT 3.5]

Since ∠A is a right angle, we know that Triangle ABC is a right triangle.

From this information, we can use the properties of special right triangles to determine the length of BC.

Since m∠B = 45°, then Triangle ABC must be a 45-45-90 triangle.

In a 45-45-90 triangle, the sides are in the ratio of x : x : x√2, where x is the length of the shorter leg and x√2 is the length of the hypotenuse.

Since the shorter leg of the triangle corresponds to side BC, and BC is the side opposite to angle B, we can see that the length of BC is x.

Therefore, the length of BC is x.

Since we only know the ratio, we know that x : x = 1 : 1.

So, the length of BC is 1.

Therefore, the length of BC is 1.