# 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?

1 answer

###### Question:

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?

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?

## Answers

Answer:5.08 ftStep-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

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