Question

a building manager needs to order 9 replacement panes that are all the same size, each similar to the window itself. at what angles should each 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 (type integers or decimals. do not include the degree symbol in your answers. use a comma to separate answers as needed.)

Explanation:

Step1: Find the third window angle

The sum of triangle angles is $180^\circ$.
$180 - 96 - 42 = 42$

Step2: Use similarity for pane angles

Similar triangles have congruent angles.
Pane angles match window angles.

Answer:

42, 42, 96

---

Additional note on dimensions (for full context):

Step3: Find scale factor of panes

There are 9 congruent similar triangles. The area scale factor is $\frac{1}{9}$, so the side scale factor is $\sqrt{\frac{1}{9}} = \frac{1}{3}$.

Step4: Calculate pane side lengths

• $40.5 \times \frac{1}{3} = 13.5$
• $60 \times \frac{1}{3} = 20$

Pane dimensions: 13.5 ft, 13.5 ft, 20 ft