triangle on the left= feet by 3 feet right triangle 9 feet by ? (?=missing angle)
Archer is sewing a triangular flag. He starts with the scale drawing on the left and plans to enlarge the flag to match the picture on the right. What will be the AREA of the completed flag? (1 point) Responses 6 square feet 6 square feet 72 square feet 72 square feet 54 square feet 54 square feet 108 square feet
To find the missing side length of the right triangle, we can use the Pythagorean Theorem:
a^2 + b^2 = c^2
Since one leg is 9 feet and the hypotenuse is 12 feet, we can plug in these values to solve for the missing leg:
9^2 + b^2 = 12^2
81 + b^2 = 144
b^2 = 63
b = √63
b ≈ 7.94 feet
Therefore, the right triangle is 9 feet by approximately 7.94 feet.
To find the area of the completed flag, we can calculate the area of both triangles and add them together:
Left Triangle Area = 0.5 * 3 * 3 = 4.5 square feet
Right Triangle Area = 0.5 * 9 * 7.94 ≈ 35.73 square feet
Total Area = 4.5 + 35.73 = 40.23 square feet
So, the area of the completed flag will be approximately 40.23 square feet.