Question

finding the perimeter of an isosceles triangle of known area
the bottom side of the flag measures 5 feet because the triangle is an isosceles triangle. because the trigonometric triangle is 1/2(5)(5)sin(36°)≈7.35. we can write the area equation to solve for x.

Explanation:

Step1: Identify the given information

We have an isosceles triangle with one - side length 5 ft and an included angle of 36°.

Step2: Recall the area formula for a triangle

The area formula for a triangle is $A=\frac{1}{2}ab\sin C$. Here, $a = 5$, $b = 5$ and $C = 36^{\circ}$, and we know $A=\frac{1}{2}(5)(5)\sin(36^{\circ})\approx7.35$. Also, if we consider the base as 5 and height as $x$, the area formula is $A=\frac{1}{2}(5)x$.

Step3: Determine the reason for writing the area equation

Since SAS (side - angle - side) information is known (two sides of length 5 and the included angle 36°), we can write the area equation to solve for other unknowns.

Answer:

The second - dropdown answer is: SAS information is known.