The inverse trigonometric ratio could be used to find the measurement of angle B, or say m∠B is given by: Option A: sin^(-1)(21/42)
Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.
In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).
The slant side is called hypotenuse.
From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.
From that angle (suppose its measure is θ),
[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\[/tex]
Here, from the perpective of the angle B, we see that the side known are AC (which is opposite to it, therefore perpendicular), and AB (whch is hypotenuse).
Although we can use pythagoras theorem to get the third side, but we'd assume we need to use only the known sides.
Since we know the perpendicular and hypotenuse, so we can either use sine ratio or cosine ratio.
Usually, we prefer top three ratio, instead of bottom three if there is a choice.
Thus, we take sine of angle B as:
[tex]\sin(m\angle B) = \dfrac{\text{Length of AC}}{\text{Length of AB}} = \dfrac{21}{42}\\\\\text{Taking inverse sin}\\\\m\angle B = \sin^{-1}\left(\dfrac{21}{42} \right)[/tex]
Thus, the inverse trigonometric ratio could be used to find the measurement of angle B, or say m∠B is given by: Option A: sin^(-1)(21/42)
Learn more about inverse trigonometric functions here:
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