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Find the missing side lengths. Leave your answers as radicals in simplest form.

Find the missing side lengths. Leave your answers as radicals in simplest form.-example-1

1 Answer

4 votes

Answer:

B x = 3, y= 3

Explanation:

Trigonometric ratios


\sf \sin(\theta)=(O)/(H)\quad\cos(\theta)=(A)/(H)\quad\tan(\theta)=(O)/(A)

where:


  • \theta is the angle
  • O is the side opposite the angle
  • A is the side adjacent the angle
  • H is the hypotenuse (the side opposite the right angle)

Given:


  • \theta = 45°
  • O =
    x
  • A =
    y
  • H =
    3√(2)


\implies \sin(45^(\circ))=(x)/(3√(2))


\implies x=3√(2)\sin(45^(\circ))


\implies x=3√(2) \cdot (√(2))/(2)


\implies x=(3√(2) √(2))/(2)


\implies x=(3 \cdot 2)/(2)=3


\implies \cos(45^(\circ))=(y)/(3√(2))


\implies y=3√(2)\cos(45^(\circ))


\implies y=3√(2) \cdot (√(2))/(2)


\implies y=(3√(2) √(2))/(2)


\implies y=(3 \cdot 2)/(2)=3

User Steve Hwang
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