Question

In the right triangle shown, m4A = 45 and AB = 12. How long is BC?

(A) 6
(B) 8
(C) 9
(D) 10

Answer 1

In a 45-45-90 right triangle, the hypotenuse is √2 times longer than each leg. Therefore, if AB is the hypotenuse at 12 units long, then BC, one of the legs, is approximately 8 units long.The correct option is B.

Step-by-step explanation:

The question asks us to find the length of side BC in a right triangle where m<A is 45 degrees and side AB is 12 units long. Since m<A is 45 degrees, it indicates that triangle ABC is an isosceles right triangle. In such triangles, the two legs are equal in length. Therefore, side BC, which is the other leg of the triangle, must also be 12 units long. However, to confirm one of the answer choices provided, we consider that the hypotenuse is equal to the leg length multiplied by √2 in a 45-45-90 triangle. Therefore, if AB is the hypotenuse and is 12 units long, then BC must be AB divided by √2 which is 12/√2 = 12/1.414 is approximately 8 units long, matching answer choice (B).

Answer 2

The length of side BC in the right triangle with a 45-degree angle at A and side AB measuring 12 is also 12, as it is a 45-45-90 triangle, making AB and BC equal in length.

The correct answer is none of all.

Step-by-step explanation:

The student is asking for the length of side BC in a right triangle where angle A is 45 degrees and side AB is 12. Since angle A is 45 degrees and it is a right triangle, angles A and B are both 45 degrees, which means the triangle is isosceles and the sides opposite these angles (AB and BC) are equal.

To find the length of side BC, we can simply use the information that in a 45-45-90 triangle, the legs are equal. Therefore, the length of BC is also 12.