Home
Class 12
MATHS
In the triangle above, the sine of ...


In the triangle above, the sine of ` x ^ @ ` is 0.6. What is the cosine of ` y^@ ` ?

Text Solution

Verified by Experts

The correct Answer is:
6 `or (3 ) /(5)`
The angles marked `x^(@)` and `y^(@)`are acute angles in a right triangle. Thus, they are complementary angles. By the complementary angle relationship between sine and cosine, it follows that `sin(x^(@)) = cos(y^(@))`. Therefore, the cosine of `y^(@)` is .6. Either .6 or the equivalent fraction `(3)/(5)` may be gridded as the correct answer.
Alternatively, since the sine of ` x ^(@)` is .6, the ratio of the side opposite the ` x ^(@)` angle to the hypotenuse is .6. The side opposite the ` x ^(@)` angle is the side adjacent to the ` y ^(@)` angle. Thus, the ratio of the side adjacent to the ` y ^(@)` angle to the hypotenuse, which is equal to the cosine of ` y ^(@)`, is equal to .6.
Promotional Banner

Similar Questions

Explore conceptually related problems

In the triangle above, sin x=0.8 and cos x=0.6. What is the area of the triangle?

In DeltaABC , The sines of the angles of a triangle are in the ratio of 4 : 5 : 6, prove that the cosines of the angles are 12 : 9 : 2.

The angles of a triangle are in the ratio 1:2:3 . What is the sine of the smallest angle?

Triangle BUG shown is an isosceles right triangle. If the length of side UG is 5 units, what is the sine of angleG ?

If the area of the triangle formed by the pair of lines 8x^2 - 6xy + y^2 = 0 and the line 2x+3y=a is 7 then a=

The right triangle above, cosx=0.8. What is the value of cosy?

In the figure above, triangleABC is a right triangle. What is the value of x?

Statement -1 : The circumcentre of the triangle formed by the lines x + y = 0 , x - y = 0 and x + 5 = 0 ( - 5 , 0) . Statement-2 : Cicumcentre of a triangle lies inside the triangle

What is the sine of /_A in the triangle below?

The orthocentre of the triangle formed by the lines x - 7y + 6 = 0, 2x - 5y - 6 = 0 and 7x + y - 8 = 0 is