Question

pane be cut in order to fit in the window? what are the dimensions of each pane? explain.
the angle measures for each pane are 96, 42, 42. (type integers or decimals. do not include the degree symbol in your answers. use a comma to separate answers as needed.)
the side lengths of each pane are 20 ft. the angles are the same by the definition of congruence. the sides are one - third the length of the entire window because identical panes fit along each side. (type integers or decimals. use a comma to separate answers as needed.)

Explanation:

Step1: Determine the angles

Since the panes are similar to the window (by the problem statement), and congruent (as they are the same size), the angles of each pane are the same as the angles of the window. Given the window - pane angle measures \(96,42,42\) (sum \(96 + 42+42=180\) which satisfies the angle - sum property of a triangle).

Step2: Determine the side lengths

The side lengths of the window are \(60\) ft, \(42\) ft, and \(40.5\) ft. Since the panes are one - third the length of the entire window (as per the problem statement), for a side length \(L\) of the window, the side length \(l\) of the pane is \(l=\frac{L}{3}\).

• For \(L = 60\) ft, \(l=\frac{60}{3}=20\) ft.
• For \(L = 42\) ft, \(l=\frac{42}{3}=14\) ft.
• For \(L = 40.5\) ft, \(l=\frac{40.5}{3}=13.5\) ft.

Answer:

The angle measures for each pane are \(96,42,42\). The side lengths of each pane are \(20\) ft, \(14\) ft, \(13.5\) ft.