Questions: 14√3 7√2 14√2 7√3

Transcript text: Post Test: Right Triangles and Trigonometry Submit Test $14 \sqrt{3}$ $7 \sqrt{2}$ $14 \sqrt{2}$ $7 \sqrt{3}$

Solution

Step 1: Identify the given information

The triangle is a right triangle with angles of 45°, 45°, and 90°. The lengths of the legs are given as 14 and 7.

Step 2: Understand the properties of a 45°-45°-90° triangle

In a 45°-45°-90° triangle, the legs are congruent, and the hypotenuse is $ \sqrt{2} $ times the length of each leg.

Step 3: Calculate the lengths of BD and BC

For BD (the hypotenuse of the smaller 45°-45°-90° triangle with leg 7): \[ BD = 7\sqrt{2} \]
For BC (the hypotenuse of the larger 45°-45°-90° triangle with leg 14): \[ BC = 14\sqrt{2} \]

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