Question

lian is making a banner for the school gym. she cut three pieces of fabric into congruent isosceles triangles, as shown. to the nearest square inch, how much fabric will she use to make all three triangles? trigonometric area formula: area = 1/2 a b * sin(c)

Explanation:

Step1: Identify triangle - side and angle values

Let \(a = 17\) in, \(b = 17\) in and \(C=74^{\circ}\)

Step2: Calculate area of one triangle

Using the formula \(A=\frac{1}{2}ab\sin(C)\), we substitute the values: \(A_1=\frac{1}{2}\times17\times17\times\sin(74^{\circ})\). Since \(\sin(74^{\circ})\approx0.9613\), then \(A_1=\frac{1}{2}\times17\times17\times0.9613=\frac{1}{2}\times289\times0.9613 = 144.5\times0.9613\approx138.9\) square - inches.

Step3: Calculate area of three triangles

\(A = 3\times A_1\), so \(A=3\times138.9 = 416.7\approx417\) square inches.

Answer:

417 square inches