Find C. Leave your answer in simplified radical form.

9514 1404 393

  7√2

Step-by-step explanation:

The triangle is a "special triangle", an isosceles right triangle. The side lengths of this triangle have the ratios 1 : 1 : √2. Multiplying these ratio values by 7, the length of the leg, you find ...

  c = 7×√2

  c = 7√2

If you like, you can go through the Pythagorean theorem and/or trigonometry to find the same thing.

  7/c = sin(45°)

  c = 7/sin(45°) = 7/(1/√2) = 7√2

Or ...

  c² = 7² + 7² = 98 . . . . using the Pythagorean theorem*

  c = √98 = 7√2

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* This requires you recognize the triangle is isosceles, so the other leg is also 7. Of course, you know that as soon as you see a 45° acute angle in a right triangle.

yes. we do proportions in probabilities.