Final answer:
a. To find the perimeter of a right triangle, use the Pythagorean theorem to find the length of the missing side, then add the lengths of all three sides. b. To find the number of trees needed, calculate the number of intervals of 10 feet that can fit along the perimeter of the field.
Step-by-step explanation:
a. Find the perimeter of the field:
To find the perimeter of a triangle, you add the lengths of all three sides. Since the field is in the shape of a right triangle, we can use the Pythagorean theorem to find the length of the missing side. The theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In this case, we have a = 35 ft and c = 80 ft. Using the formula, we can solve for b: b = sqrt(c^2 - a^2). Plugging in the values, we have b = sqrt(80^2 - 35^2) = sqrt(6400 - 1225) = sqrt(5175) ≈ 71.94 ft.
Now, we can find the perimeter by adding all three sides: perimeter = a + b + c = 35 ft + 71.94 ft + 80 ft ≈ 186 ft. Therefore, the perimeter of the field is about 186 feet.
b. You are going to plant dogwood seedlings around the field's edge:
To find the number of trees needed, we need to calculate the number of intervals of 10 feet that can fit along the perimeter of the field. The perimeter of the field is 186 feet, so we divide it by 10 to get the number of intervals: intervals = 186 ft / 10 ft = 18.6 intervals. Since we can't have a fraction of an interval, we round up to the nearest whole number, which gives us the number of trees needed: trees = ceil(18.6) ≈ 19 trees.