In right triangle ABC below, what is the sine of <A?

TRiangle has 7 cenimeters and 24 centimeters

If the triangle had sides 7 and 24 adjacent to the right angle, then the hypothenuse is sqrt(7^2+24^2)=25 by Pythagoras theorem.

The sin of angle θ adjacent to the side 7 has an opposite side of 24 over the hypothenuse of 25, so
sin(θ)=24/25.

Similarly, the sin of the angle φ is the opposite side 7 divided by the hypothenuse of 25 to give 7/25.

thank u

To find the sine of angle A in the right triangle ABC, we need to know the lengths of the sides of the triangle.

From the information given, we know the triangle has sides measuring 7 centimeters and 24 centimeters. However, we don't have the length of the third side, which we'll call side c.

To find the sine of angle A, we can use the definition of sine which is the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, the side opposite angle A is side b (length of 7 cm) and the hypotenuse is side c (unknown).

To find side c, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Using the Pythagorean theorem, we can solve for c:

c^2 = a^2 + b^2
c^2 = 24^2 + 7^2
c^2 = 576 + 49
c^2 = 625
c = √625
c = 25

Now that we know the length of side c (hypotenuse), we can find the sine of angle A:

sine(A) = opposite/hypotenuse
sine(A) = b/c
sine(A) = 7/25

Therefore, the sine of angle A in the right triangle ABC is 7/25.