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