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 = $\frac{1}{2}absin(c)$

Explanation:

Step1: Identify the values for the formula

For each isosceles - triangle, let \(a = 17\) in, \(b = 17\) in, and \(C=74^{\circ}\).

Step2: Calculate the area of one triangle

Using the formula \(A=\frac{1}{2}ab\sin(C)\), substitute \(a = 17\), \(b = 17\), and \(C = 74^{\circ}\). First, find \(\sin(74^{\circ})\approx0.9613\). Then \(A_1=\frac{1}{2}\times17\times17\times0.9613=\frac{1}{2}\times289\times0.9613\approx139.01\) square inches.

Step3: Calculate the area of three triangles

Since there are three congruent triangles, \(A = 3\times A_1\). So \(A=3\times139.01 = 417.03\approx417\) square inches.

Answer:

417 square inches