The angle of B is 56.2 degrees
Solution:
Given is a right angled triangle ABC
From given figure,
AB = 9
CB = 5
We have to find the angle of B
Let the angle of B be [tex]\theta[/tex]
By definition of cosine,
[tex]cos \theta = \frac{adjacent}{hypotenuse}[/tex]
Here, adjacent = CB and hypotenuse = AB
Therefore,
[tex]cos \theta = \frac{5}{9}\\\\cos \theta = 0.556[/tex]
Taking cos inverse on both sides,
[tex]\theta = cos^{-1}(0.556)\\\\\theta = 56.22038005 \approx 56.22[/tex]
Thus the angle of B is 56.22 degrees
Measure of angle B in the given right triangle ABC is 56.25°.
Given in the question,
By applying cosine rule in ΔABC,
cos(∠B) = [tex]\frac{\text{Adjacent side}}{\text{Opposite side}}[/tex]
= [tex]\frac{5}{9}[/tex]
[tex]\angle B =\text{cos}^{-1}(\frac{5}{9} )[/tex]
= 56.251
≈ 56.25°
Therefore, measure of angle B will be 56.25°.
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