In triangle ABC, angle A = 90 degrees, angle B = 30 degrees, AB = 6cm. Find the sides of the triangle.

Three points of the plane that do not lie on one straight line, connected by segments are called a triangle. In this case, the points are the vertices of the triangle, and the segments are its sides.

If one of the angles in a triangle is equal to 90º, then this triangle is right-angled.

To calculate the hypotenuse BC, it is most convenient to apply the cosine theorem, since the length of the hypotenuse AB and the degree measure of the angle B are known. The cosine of an acute angle of a right triangle is the ratio of the adjacent leg to the hypotenuse:

cos B = AB / BC;

BC = AB / cos B;

cos 30º ≈ 0.866;

BC = 6 / 0.866 ≈ 9.2.

To calculate the length of the AC leg, we use the sine theorem.

The sine of an acute angle of a right triangle is the ratio of the opposite leg to the hypotenuse:

sin B = AC / BC;

AC = BC · sin B;

sin 30º = 1/2;

AC = 9.2 1/2 = 9.2 / 2 = 4.6 cm.

Answer: The length of the speaker is 4.6 cm, the length of the BC is 9.2 cm.