If two angles of an isosceles triangle measure 35 degrees each, then the third angle must be:
180 - 35 - 35 = 110 degrees
Since the triangle is isosceles, the two equal angles must be opposite the two equal sides. Therefore, the triangle has two equal sides and one unequal side. Let's call the length of the unequal side "x".
By the triangle sum property, we know that the sum of the angles in a triangle is 180 degrees. Therefore, we can set up an equation:
35 + 35 + 110 = 180
Simplifying, we get:
180 = 180
This equation is true, which means that the given angles do form a valid triangle.
Since the triangle is isosceles, we know that the length of the two equal sides is equal. Let's call the length of each equal side "y". We can use trigonometry to find the length of the equal sides:
y = x * sin(35)
Now we can find the perimeter of the triangle:
Perimeter = 2y + x
Perimeter = 2(x * sin(35)) + x
Perimeter = x(2sin(35) + 1)
Substituting x = 18, we get:
Perimeter = 18(2sin(35) + 1)
Perimeter ≈ 48.26 feet (rounded to two decimal places)
Therefore, the perimeter of the isosceles triangle is approximately 48.26 feet.