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Mathematics

1 answer:

Debora [2.8K]3 years ago

5 0

Answer:

$\angle B=41.81^\circ$

Step-by-step explanation:

<u>Trigonometric Ratios</u>

The ratios of the sides of a right triangle are called trigonometric ratios.

The longest side of the triangle is called the hypotenuse and the other two sides are the legs.

The sine ratio relates the opposite side of an angle of the triangle with the hypotenuse:

$\displaystyle \sin B=\frac{\text{opposite leg}}{\text{hypotenuse}}$

Here, the opposite leg to angle B is the side CA=2, and the hypotenuse is the side AB=3, thus:

$\displaystyle \sin \angle B=\frac{2}{3}=0.667$

Calculating the inverse sine function:

$\angle B=\arcsin (0.667)$

$\boxed{\angle B=41.81^\circ}$

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