# The legs of a right triangle are √15 and 1 find the sine of the smallest angle of this triangle.

In order for us to find the hypotenuse of the AC, we will use the Pythagorean theorem which is applicable in a right-angled triangle. The Pythagorean theorem sounds like this: the square of the hypotenuse is equal to the sum of the squares of the legs.

c ^ 2 = a ^ 2 + b ^ 2, where a and b are the legs of a right triangle, and c is the hypotenuse in a right triangle.

Find the hypotenuse AC

In our case, the theorem will look like this: AC2 = AB2 + BC2. Let’s substitute the known values into this formula such as the AB leg which is equal to √15 cm and the second BC leg which is 1 cm and find the AC hypotenuse in the right-angled triangle ABC, then we get:

AC ^ 2 = AB ^ 2 + BC ^ 2;

AC ^ 2 = (√15 cm) ^ 2 + BC ^ 2;

AC ^ 2 = (√15 cm) ^ 2 + (1 cm) ^ 2;

We bring √15 cm to the square, we get:

AC ^ 2 = 15 cm2 + (1 cm) 2;

Now let’s bring 1 cm to the square, we get:

AC ^ 2 = 15 cm2 + 1 cm2;

AC ^ 2 = 16 cm2;

Find an AC without a square, we get:

AC = √16cm2 = 4 cm.

And so we found the hypotenuse AC.

Find sinA and sinC

sin A = BC / AC = 1/4 = 0.25;

sin C = AB / AC = √15 / 4 = 0.968;

We get that the sine of angle A is 0.25, which means that its angle is about 14 degrees, and this is the smallest angle in the ABC triangle.

Answer: The sine of the smallest angle of this triangle is 0.25.