Right triangle ABC is shown the sine of <a is 0.53. What is the cosine of <B
To find the cosine of angle B, we first need to find the length of the sides of the triangle.
Given that sine of angle A is 0.53, we can use the definition of sine in a right triangle:
sin(A) = opposite/hypotenuse
0.53 = opposite/1
opposite = 0.53
Now we can use the Pythagorean theorem to find the length of the remaining side in the triangle:
a^2 + b^2 = c^2
0.53^2 + b^2 = 1^2
0.2809 + b^2 = 1
b^2 = 1 - 0.2809
b^2 = 0.7191
b = √0.7191
b ≈ 0.848
Now that we have the length of the adjacent side (0.848) and the hypotenuse (1), we can find the cosine of angle B using the definition of cosine in a right triangle:
cos(B) = adjacent/hypotenuse
cos(B) = 0.848/1
cos(B) = 0.848
Therefore, the cosine of angle B is 0.848.