Answer:
[tex]\angle B=\cos^{-1}\left(\dfrac{6.3}{9.8}\right)\\ \\\angle B=\sin^{-1}\left(\dfrac{7.5}{9.8}\right)[/tex]
Step-by-step explanation:
Consider right triangle ABC with right angle C.
In this triangle,
Write trigonometric functions:
[tex]\cos \angle B=\dfrac{BC}{AB}=\dfrac{6.3}{9.8}\\ \\\sin \angle B=\dfrac{AC}{AB}=\dfrac{7.5}{9.8}[/tex]
Hence,
[tex]\angle B=\cos^{-1}\left(\dfrac{6.3}{9.8}\right)\\ \\\angle B=\sin^{-1}\left(\dfrac{7.5}{9.8}\right)[/tex]
The required value of [tex]\theta[/tex] is [tex]cos^{-1}(\frac{6.3}{9.8} )[/tex] and [tex]sin^{-1}(\frac{7.5}{9.8})[/tex].
Given that,
Triangle ABC is shown. Angle BCA is a right angle.
The length of hypotenuse BA is 9.8 inches,
The length of CB is 6.3 inches,
and the length of CA is 7.5 inches.
We have to find,
The expressions can be used to find mâ ABC.
According to the question,
In triangle ABC with right angle c.
Sine is the ratio of the length of the side that is opposite that angle, to the length of the longest side of the triangle (the hypotenuse),
Sin[tex]\theta[/tex] = [tex]\frac{BC}{AB}[/tex]
Sin[tex]\theta[/tex] = [tex]\frac{7.5}{9.8}[/tex]
[tex]\theta[/tex] = [tex]sin^{-1}(\frac{7.5}{9.8})[/tex]
And,
The cosine is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.
Cos[tex]\theta[/tex] = [tex]\frac{AC}{AB}[/tex]
Cos[tex]\theta[/tex] = [tex]\frac{6.3}{9.8}[/tex]
[tex]\theta[/tex] = [tex]cos^{-1}(\frac{6.3}{9.8} )[/tex]
Hence, The required value of [tex]\theta[/tex] is [tex]cos^{-1}(\frac{6.3}{9.8} )[/tex] and [tex]sin^{-1}(\frac{7.5}{9.8})[/tex].
For the more information about Trigonometry click the link given below.
https://brainly.com/question/25549088
