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Find the value of each variable. (Simplify your answers. Type exact answers, using radicals as needed.) a =...

Find the value of each variable.
(Simplify your answers. Type exact answers, using radicals as needed.)
a = □, b = □, c = □, and d = □

Answer

To solve for the variables in the right triangle, we use trigonometric ratios and properties of special triangles:

  1. a: Since the triangle is a 45°-45°-90° triangle, the legs are equal. Therefore, a = 13.
  2. b: In a 30°-60°-90° triangle, the hypotenuse is twice the shorter leg. Therefore, b = 13√2.
  3. c: In a 45°-45°-90° triangle, the legs are equal, so c = 13.
  4. d: In a 30°-60°-90° triangle, the longer leg is √3 times the shorter leg. Therefore, d = 13√3.

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