# The legs of a right triangle are 20 and 15. Find the sine of the smallest angle of this triangle

May 31, 2020 | Education

| Since the triangle is rectangular, we can apply the Pythagorean theorem:

AB2 = BC2 + AC2

AB ^ 2 = 15 ^ 2 + 20 ^ 2

AB ^ 2 = 225 + 400 = 625

AB = 25

The smaller angle lies opposite the smaller side, 15 <20, therefore the sine of the smaller angle will be equal to the ratio of the smaller side to the hypotenuse, i.e. 15/25 = 3/5 = 0.6

Answer: 0.6

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