The sum of the all the angle in a triangle is equal to the 180 degrees.
The relationship which is true for the given triangle is,
[tex]\sin (B)=\cos (90-B)[/tex]
Thus the option B is the correct option.
What is the value of sine in right angle triangle?
In a right angle triangle the ratio of opposite side to the hypotenuse side is equal to the angle of sine.
Given information-
The given triangle in the figure [tex]\Delta ABC[/tex] is right angle triangle.
[tex]m\angle C[/tex] is the right angle measure of 90 degrees.
The sum of the all the angle in a triangle is equal to the 180 degrees. Thus,
[tex]m\angle C+m\angle A +m\angle B=180[/tex]
Put the value of [tex]m\angle C[/tex] as,
[tex]90+m\angle A +m\angle B=180\\m\angle A +m\angle B=180-90\\m\angle A +m\angle B=90[/tex]
Thus the sum of measure of [tex]m\angle A[/tex] and [tex]m\angle B[/tex] is 90 degrees.
Solve further as,
[tex]m\angle A =90-m\angle B[/tex]
Let the above equation as equation number 1.
In a right angle triangle the ratio of opposite side to the hypotenuse side is equal to the angle of sine. Thus,
[tex]Sin(B)=\dfrac{b}{c}[/tex]
Similarly,
[tex]\cos(A)=\dfrac{b}{c}[/tex]
Hence for the right angle triangle,
[tex]\sin (B)=\cos (A)[/tex]
Put the value of angle form equation 1 to the above equation as,
[tex]\sin (B)=\cos (90-B)[/tex]
Hence the relationship which is true for the given triangle is,
[tex]\sin (B)=\cos (90-B)[/tex]
Thus the option B is the correct option.
Learn more about the right angle triangle here;
https://brainly.com/question/64787
