Find the exact value of sinA where a=9 and b=10 and angle C is a right angle.
a. sin A= 9/sqrt 181, cos A= sqrt 181/10
b. sin A= sqrt 181/9, cos A= 10/sqrt 181
c. sin A= 9/sqrt 181, cos A= 10/sqrt 181
d. sin A=sqrt181/10, cos A= 9/sqrt 181
sin A= 9/sqrt181, cosA=10/sqrt181
Did you sketch the right triangle?
To find the exact value of sinA, we can use the trigonometric relationship in a right triangle involving the sides a, b, and the angle C.
In this case, we are given that a = 9, b = 10, and angle C is a right angle.
Using the Pythagorean theorem, we can determine the length of side c (the hypotenuse):
c^2 = a^2 + b^2
c^2 = 9^2 + 10^2
c^2 = 81 + 100
c^2 = 181
Now, let's find the exact value of sinA:
sinA = opposite/hypotenuse = a/c = 9/√181
Therefore, the correct answer is option a: sin A = 9/√181, cos A = √181/10.
To find the exact value of sin(A), you need to use the given information about the lengths of the sides of a right triangle.
In a right triangle, the side opposite angle A is given by side a, and the hypotenuse is given by side b. The sine of angle A is defined as the ratio of the length of the side opposite angle A to the length of the hypotenuse.
Using the given values, a = 9 and b = 10, we can substitute them into the formula for sine:
sin(A) = a/b
sin(A) = 9/10
However, to simplify the answer, we need to rationalize the denominator by multiplying both the numerator and denominator by the square root of 181:
sin(A) = (9/10) * (sqrt 181 / sqrt 181)
sin(A) = (9 * sqrt 181) / (10 * sqrt 181)
Now we can see that the numerator and denominator both have the square root of 181, so they can cancel out, leaving us with:
sin(A) = 9 / 10
Therefore, the correct option is a. sin A = 9/sqrt 181, cos A = sqrt 181/10.