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

May 31, 2020 | Education

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

AB ^ 2 = BC ^ 2 + CA ^ 2

AB ^ 2 = (√15) ^ 2 + 1 ^ 2

AB ^ 2 = 15 + 1 = 16

AB = 4

The smallest angle lies opposite the smallest side (by the theorem on the ratio of sides and angles).

Then the smallest angle is ∠ABC (since 1 <√15).

sin (∠ABC) = AC / AB = 1/4 = 0.25

Answer: the sine of the smallest angle is 0.25

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