The legs of a right-angled triangle are 4 and 3. find the sine of the smallest angle of this triangle.

| April 19, 2021 | education

To solve this problem, remember that the sine of an acute angle in a right-angled triangle is the ratio of the opposite leg to the hypotenuse. Thus, to find the sine, we need to calculate the hypotenuse. Knowing that the length of the leg of one leg is 4 cm, and the second – 3 cm, we calculate the hypotenuse by the Pythagorean theorem. Pythagoras’ theorem: the square of the hypotenuse is equal to the sum of the squares of the legs.
c ^ 2 = 4 * 4 + 3 * 3 = 16 + 9 = 25.
c = √25 = 5 cm.
Let us recall the property of the sides and angles of a triangle. The smallest angle lies in the triangle opposite the smaller side. Thus, we must calculate the sine of the angle – A, which lies opposite the leg 3 cm long.
Then the sine of angle A is equal to.
sine A = 3/5.
Answer: 3/5.



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