The side lengths for delta ABC are a, b, and c The height of the triangle is h,

Question

The side lengths for delta ABC are a, b, and c The height of the triangle is h, and CD = x. Complete the steps below to prove the Law of Cosines. When filling in the blanks, you may use the letters a, b, c, x, and h Part1: Use the Pythagorean Theorem to find c^2. c^2 = b^2 - x^2 c^2 = x^2 + h^2 c^2 = (b-x)^2 + h^2 c^2 = (a-x)^2 + h^2 Part 2: Use the answer from Part 1 to fill in the blanks. C^2 = X^2 + h^2 + Part 3: Use the Pythagorean Theorem to find a^2. a^2 = x^2 + h^2 a^2 = (b-x)^2 + h^2 a^2 = (c-x)^2 + h^2 a^2 = b^2 - c^2 Part 4: Use the answers from Parts 2 and 3 to fill in the blanks. c^2 = Part 5: Use trigonometry to fill in the blank. x = cos C Part 6: Use the answers from Parts 4 and 5 to fill in the blanks. c^2 =

Explanation / Answer

Part 1: correct

Part2 : c^2 = h^2 +( b-x)^2

= h^2 +b^2 +x^2 -2bx

Part3 : a^2 = h^2 +x^2

Part4 : substitute value of x^2

c^2 = a^2 + b^2 -2bx

Part 5: x = acosC

Part C : c^2 = a^2 +b^2 -2a*bcosC

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