Respuesta :

Using the trigonometry ratio and Pythagorean Theorem, the value of b in the triangle is: 4.

Recall:

  • The trigonometry ratio is used in solving a right triangle, having, hypotenuse, adjacent, and the opposite side, given a reference angle.
  • Trigonometry ratios are: SOH CAH TOA
  • Pythagorean Theorem is given as: [tex]c^2 = a^2 + b^2[/tex], where c is the longest side (hypotenuse).

Given the trigonometry ratio of sin A = 3/5

Recall that, sin ∅ = opp/hyp (SOH)

Thus, this means that, in sin A = 3/5,

  • A = ∅
  • 3 = opposite side, which corresponds to a in the given triangle.
  • 5 = hypotenuse, which corresponds to c in the given triangle.
  • b is therefore the adjacent side

Thus, find the value of b by applying the Pythagorean theorem.

[tex]b = \sqrt{c^2 - a^2}[/tex] (Pythagorean Theorem)

  • Substitute

[tex]b = \sqrt{5^2 - 3^2}\\\\\mathbf{b = 4}[/tex]

Therefore, using the trigonometry ratio and Pythagorean Theorem, the value of b in the triangle is: 4.

Learn more about Trigonometry ratios on:

https://brainly.com/question/4326804

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