Answer:
0.73 rad (approx.), or 42 degrees
Step-by-step explanation:
The "ratio for the opposite leg divided by the hypotenuse is 0.67" implies that
sin B = 0.67. To find the measure of the angle B, we need only to find
arcsin 0.67 = B. Using a calculator, arcsin 0.67 = 0.73 rad (approx.), or
42 degrees.
The reasonable approximation for angle B will be [tex]42.06^\circ[/tex].
Given,
Angle B is an acute angle of the given right triangle.
The ratio of opposite leg to hypotenuse is 0.67 .
We have to find the value of angle B.
Since the side opposite to angle B is perpendicular.
Here,
[tex]\dfrac{\rm Perpendicular}{\rm hypotenuse} =0.67[/tex]
Since the ratio of perpendicular to hypotenuse will be known as sinusoidal (sin) of the angle consisting the hypotenuse. So
[tex]\rm sinB=\dfrac{\rm Perpendicular}{\rm hypotenuse}[/tex]
Now, [tex]\rm sinB=0.67[/tex]
Or,
[tex]\angle \rm B=sin^{-1}\ 0.67[/tex]
[tex]\angle \rm B=42.06^\circ[/tex]
Hence the value of angle B is 42 degrees.
For more details on inverse trigonometric function follow the link:
https://brainly.com/question/1143565
