Final answer:
To find the area of the triangle, we can use the formula ½ * base * height. By applying the Pythagorean theorem, we can find the missing side length and then substitute the values into the formula. The approximate area of the triangle is 279.54 square inches.
Step-by-step explanation:
To find the area of a triangle, we can use the formula ½ * base * height. Given the dimensions a = 27 in and c = 34 in, we need to find the height. We can do this by applying the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
We can solve for b using the formula: b = √(c² - a²). Substituting the given values, we have b = √(34² - 27²) = √(1156 - 729) = √427 ≈ 20.67 in.
Now we can substitute the values for the base and height into the area formula: Area = ½ * base * height = ½ * 27 in * 20.67 in ≈ 279.54 in². Therefore, the approximate area of the triangle is 279.54 square inches.