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Kendrick is trying to determine if a painting he wants to buy will fit in the space on his wall. If the rectangular frame's diagonal is 50 inches and forms a 36. 87° angle with the bottom of the frame, what is its height? Round your answer to the nearest inch. 28 inches 30 inches 38 inches 40 inches.

Respuesta :

To solve the problem we must know about the Sine function of trigonometry.

What is Sine (Sinθ)?

The Sine or Sinθ in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,

[tex]\rm{Sine(\theta) = \dfrac{Perpendicular}{Hypotenuse}[/tex]

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The hypotenuse is the longest side of the triangle.

The height of the painting is 30 inches.

Given to us

  • The rectangular frame's diagonal is 50 inches, BD = 50
  • The diagonal forms a 36. 87° angle with the bottom of the frame,        ∠C=36. 87°

Using the Sine function of trigonometry,

[tex]\rm{Sine(\theta) = \dfrac{Perpendicular}{Hypotenuse}[/tex]

Substitute the value,

[tex]\rm{Sin(\angle DBC) = \dfrac{DC}{BD}[/tex]

[tex]Sin(36.87^o) = \dfrac{height}{50}\\\\BD = Sin(36.87^o)\times {50}\\\\BD = 30\ inches[/tex]

Hence, the height of the painting is 30 inches.

Learn more about Sine:

https://brainly.com/question/21286835

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