Find m∠B, rounded to the nearest degree.

• : [tex]\sin(\angle B) = \dfrac{\text{opp}}{\text{hyp}} [/tex]
  
  [tex]\sin(\angle B) = \dfrac{4}{5} [/tex]
  
  [tex]\angle B = \sin^{-1}\bigg(\dfrac{4}{5} \bigg)[/tex]
  
  [tex]\angle B = 53.15 \textdegree[/tex]
  
• KarpaT:

  The measure of ∠B of the right triangle is 53.13°.

  What is trigonometry?

  Trigonometry is mainly concerned with specific functions of angles and their application to calculations. Trigonometry deals with the study of the relationship between the sides of a triangle (right-angled triangle) and its angles.

  For the given situation,

  The measure of ∠B can be found by

  [tex]sin B=\frac{opposite}{hypotenuse}[/tex]

  From the diagram, Opposite side = 4 units

  Hypotenuse side = 5 units

  Thus on substituting the above values,

  ⇒ [tex]sin B=\frac{4}{5}[/tex]

  ⇒ [tex]B = sin^{-1} (0.8)[/tex]

  ⇒ [tex]B=53.13[/tex]

  Hence we can conclude that the measure of ∠B of the right triangle is 53.13°.

  Learn more about trigonometry here

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