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

March 27, 2021 | education

| 1. According to the condition of the problem, the angle A is 90 *, the leg AB is 6 cm, the angle B is 30 *, so the leg AC and the hypotenuse can be calculated using trigonometric formulas.

2. Find the length of the AC leg.

AC: AB = tg 30 * = 1/3 ^ 1/2;

AC = AB * 1/3 ^ 1/2 = 6 cm: 3 ^ 1/2 cm = 6 cm: 1.73 = 3.45 cm.

3. Let’s calculate what the hypotenuse BC is equal to.

AB: BC = cos 30 *;

BC = AB: cos 30 * = 6 cm: 3 ^ 1/2/2 = 12 * 3 ^ 1/2 cm = 12 cm * 1, 73 = 20.76 cm.

Answer: In the ABC triangle, the AC side is 3.45 centimeters,

the side of the sun is 20.76 centimeters.

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