The lid of a grand piano is propped open by a
supporting arm, as shown in the diagram at
right. Carson knows that the supporting arm
is 2 feet long and makes a 60° angle with the
piano. He also knows that the piano lid
makes a 23° angle with the piano. How wide
is the piano?

Question

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opudodennis opudodennis · Answer 1 · 2020-04-14T02:22:05+02:00

Answer:

5.08 ft

Step-by-step explanation:

-This is a shape formed by the lid, piano amd supporting arm i a triangle.

-The piano's width corresponds to the missing angle and the ∠23° corresponds to the length of the supporting arm.

#We apply the Law of Sines to Calculate the piano's width:

[tex]\frac{a}{Sin\ A}{=\frac{b}{Sin \ B}=\frac{c}{Sin \ C }\\[/tex]

We substitute as follows:

[tex]\therefore \frac{2}{Sin \ 23\textdegree}=\frac{W}{Sin (180-23-60)}\\\\W=\frac{2}{Sin \ 23}\times Sin \ 97\\\\=5.0805\approx 5.08\ ft[/tex]

Hence, the piano's width is 5.08 ft