Question

Daniel is standing outside his apartment building because his cable company cut off his service. He is watching his second favorite show through his neighbors window. The cosine of the angle of elevation from Daniel to the apartment is 15/12. He suddenly notices that his neighbor on the next floor is watching his favorite show and adjusts his view so that his angle of elevation is double what it was before. Dind the value of the sine of the new angle of elevation.

Answer 1

The value of the sine of the new angle of elevation is 15i/8

Sine of the New Angle of Elevation

Let the angle of elevation of Daniel's neighbors apartment be Ф. When he adjusts to view on the next floor, the elevation of the apartment is double the initial. So, this new angle of elevation is α = 2Φ.

Since we require sinα = sin2Φ = 2sinΦcosΦ

Since the cosine of the angle of elevation from Daniel to the apartment is 15/12, cosΦ = 15/12

Using trigonometric identities,

sin²Ф + cos²Ф = 1

sinФ = √(1 - cos²Ф)

Substituting the value of the cosФ into the equation, we have

sinФ = √(1 - cos²Ф)

sinФ = √(1 - (15/12)²)

sinФ = √(1 - (225/144))

sinФ = √([144 - 225]/144))

sinФ = √(-81/144)

sinФ = 9i/12

sinФ = 3i/4

So, sinα = sin2Φ

= 2sinΦcosΦ

= 2 × 3i/4 × 15/12

= 15i/8

So, the value of the sine of the new angle of elevation is 15i/8

Learn more about sine of an angle here:

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