One of the base angles of an isosceles triangle measures 68.6°. The base of the triangle measures 12 centimeters. What is the perimeter of the triangle? Round intermediate results to 3 decimal places and the final answer to 1 decimal place.

44.9 centimeters

Step-by-step explanation:

We're looking for the perimeter, but we only know 1 side; we need to know all three. First, let's figure out what a is with this equation: a = √h² + (c/2)². Substitute h for 15.31 and c for 12.

a = √15.31² + (12/2)²

Step 1: Divide 12 by 2 to get 6.

a = √15.31² + 6²

Step 2a: The square of 15.31 is 234.3961. For convenience, I'll round this to 234.396.

a = √234.396 + 6²

Step 2b: The square of 6 is 36.

a = √234.396 + 36

Step 3: Add 234.396 and 36 to get 270.396.

a = √270.396

Step 4: The square root of 270.396 is 16.4437222. For convenience, I'll round this to 16.444.

a = 16.444

Note: This value is the same for side b, since this is an isosceles triangle.

Now, all we need to do is add 16.444 (twice) and 12 to get our perimeter.

(16.444 * 2) + 12

Step 5: Multiply 16.444 by 2 to get 32.888.

32.888 + 12

Step 6: Add 32.888 to 12 to get 44.888.

44.888

Step 7: Now the answer above is the actual answer, but we need to round it to one decimal place. 8 is greater than 5, so this rounds up to 44.9.

The perimeter of this triangle is 44.9 centimeters.