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Find cos (B) in the triangle

Find Cos B In The Triangle class=

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theleangreenbean

Basic Trigonometric Ratios

We can identify the sides of a right triangle by describing their location in relation to a given angle.

  • The "hypotenuse" is the longest side of a right triangle. It is opposite the right angle.
  • The "opposite" is the side that the angle does not touch.
  • The "adjacent" is the side that the angle does touch, that is not the hypotenuse.

There are three basic trigonometric ratios:

  • The sine ratio: [tex]\sin\theta=\dfrac{opposite}{hypotenuse}[/tex]
  • The cosine ratio: [tex]\cos\theta=\dfrac{adjacent}{hypotenuse}[/tex]
  • The tangent ratio: [tex]\tan\theta=\dfrac{opposite}{adjacent}[/tex]

We use theta (θ) to represent an angle.

Solving the Question

We are asked to find [tex]\cos(\beta)[/tex] in the triangle.

[tex]\cos\theta=\dfrac{adjacent}{hypotenuse}[/tex]

The side adjacent to β measures 8 units.

The hypotenuse of the right triangle measures 17 units.

[tex]\cos\beta=\dfrac{8}{17}[/tex]

Answer

Therefore, [tex]\cos\beta=\dfrac{8}{17}[/tex].

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