279 in² is the answer
To find the approximate area of a right triangle, you can use the formula:
Area = (1/2) * base * height
In your case, "a" is the base and "c" is the hypotenuse. To find the height, you can use the Pythagorean theorem since it's a right triangle:
c^2 = a^2 + height^2
34^2 = 27^2 + height^2
1156 = 729 + height^2
Now, subtract 729 from both sides:
height^2 = 1156 - 729
height^2 = 427
Take the square root of both sides:
height ≈ √427
height ≈ 20.71 inches (rounded to two decimal places)
Now, you can find the area:
Area = (1/2) * a * height
Area = (1/2) * 27 in * 20.71 in
Area ≈ 277.695 square inches
Rounding to the nearest whole number, the approximate area of the triangle is 278 square inches. None of the provided answer choices exactly match this value, but the closest one is 279 in². So, 279 in² is the closest approximate area among the options given.