Question

Solve for an angle in right triangles

Answer 1

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 $\theta$

By definition of cosine,

$cos \theta = \frac{adjacent}{hypotenuse}$

Here, adjacent = CB and hypotenuse = AB

Therefore,

$cos \theta = \frac{5}{9}\\\\cos \theta = 0.556$

Taking cos inverse on both sides,

$\theta = cos^{-1}(0.556)\\\\\theta = 56.22038005 \approx 56.22$

Thus the angle of B is 56.22 degrees