Question

Determine each length in right triangle ABC.

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Right triangle ABC with right angle at vertex B. Point D lies on side AC. A dashed segment BD is drawn. Angles BAD and BCD both measure 45 degrees. Angle ADB is a right angle. Segments AD and CD both are labeled 8.

Answer 1

In a right triangle ABC with right angle at vertex B, the lengths of AB, AD, BD, BC, and CD can be determined using the Pythagorean Theorem. AB = 8 sqrt(2), AD = 8, BD = 8, BC = 8 sqrt(2), and CD = 8.

Step-by-step explanation:

In a right triangle ABC with right angle at vertex B, point D lies on side AC. Angles BAD and BCD both measure 45 degrees. Angle ADB is a right angle. Segments AD and CD are both labeled 8.

To determine the lengths in the triangle, we can use the Pythagorean Theorem. Since angle BAD is 45 degrees, triangle ADB is a 45-45-90 triangle.

Therefore, the hypotenuse AB is equal to 8 times the square root of 2, and the legs AD and BD are both equal to 8.

Similarly, since angle BCD is 45 degrees, triangle BDC is also a 45-45-90 triangle. Therefore, the hypotenuse BC is equal to 8 times the square root of 2, and the legs CD and BD are both equal to 8.

Therefore, the lengths in the right triangle ABC are: AB = 8 sqrt(2), AD = 8, BD = 8, BC = 8 sqrt(2), and CD = 8.