Priyanka's new home had a rectangular shaped glass window in the kitchen that gave her a beautiful view of the front garden. The window pane was 40 inches in length and 24 inches in width. If a line DE is drawn at an angle of 30° to AD, the length of DE will be
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Given: The length of the window pane = 40 inches
The width of the window pane = 24 inches
DE is at an angle of 30° to AD.
To find: The length of DE
Solution: From the given figure, we can understangle that the angle DAE is a right angle. So we can use the Pythagoras' theorem and the trigonometric functions to determine the length of DE.
Accordingly,
cos 30° = AD/DE
Here, we know that AD = 24 inches since it is the width of the window pane.
∴ cos 30° = 24/DE
⇒ √3/2 = 24/DE
⇒ DE = 24 ×2/√3
⇒ DE = 48√3/3
⇒ DE = 16√3 inches
Answer: 16√3 inches
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