Question

the flag is an isosceles triangle. the bottom side of the flag measures 5 feet because the inangle is. because, the trigonometric triangle formula is used to calculate that the area is 1/2(5)(5)sin(36°)=7.35 square feet. recalling that this triangle is isosceles, we can write the area equation to solve for x. =1/2(x)(5)sin(). solving for x and adding this value to the length of the other sides, the perimeter = (rounded to the nearest tenth)

Explanation:

Step1: Recall area formula for triangle

The area formula for a triangle is $A=\frac{1}{2}ab\sin C$. We know $A = 7.35$, $a=x$, $b = 5$ and $C=36^{\circ}$. So the equation is $7.35=\frac{1}{2}(x)(5)\sin(36^{\circ})$.

Step2: Solve for $x$

First, simplify the right - hand side. $\sin(36^{\circ})\approx0.5878$. The equation becomes $7.35=\frac{1}{2}(x)(5)(0.5878)$. Then $\frac{1}{2}(5)(0.5878)=1.4695x$. So $x=\frac{7.35}{1.4695}\approx5.0$.

Step3: Calculate perimeter

The isosceles triangle has two sides of length $x$ and one side of length 5. The perimeter $P=2x + 5$. Substitute $x\approx5.0$ into the formula, $P=2\times5.0+5=15.0$ feet.

Answer:

15.0 feet