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alexandr402 [8]
3 years ago
11

One of the base angles of an isosceles triangle measures 68.6°. The base of the triangle measures 12 centimeters. What is the pe

rimeter of the triangle? Round intermediate results to 3 decimal places and the final answer to 1 decimal place.
Mathematics
1 answer:
Svetradugi [14.3K]3 years ago
4 0

Answer:

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

<em>Step 1: Divide 12 by 2 to get 6.</em>

a = √15.31² + 6²

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

a = √234.396 + 6²

<em>Step 2b: The square of 6 is 36.</em>

a = √234.396 + 36

<em>Step 3: Add 234.396 and 36 to get 270.396.</em>

a = √270.396

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

a = 16.444

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

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

(16.444 * 2) + 12

<em>Step 5: Multiply 16.444 by 2 to get 32.888.</em>

32.888 + 12

<em>Step 6: Add 32.888 to 12 to get 44.888.</em>

44.888

<em>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.</em>

The perimeter of this triangle is 44.9 centimeters.

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