In a right-angled triangle ABC, where C is a right angle, AB = 18, angle B = 60. Find the speaker

Since ∆ABC is rectangular, then ∠В + ∠A = 90 °. Then we find ∠A.

∠A = 90 ° – ∠В = 90 ° – 60 ° = 30 °.

Or by the theorem on the sum of the angles of a triangle: ∠В + ∠A + ∠С = 180 °, it follows that ∠A = 180 ° – (∠В + ∠С) = 180 ° – (60 ° + 90 °) = 180 ° – 150 ° = 30 °.

In a right-angled triangle, the side opposite to an angle of 30 ° is half the hypotenuse, then BC = ½ * AB = ½ * 18 = 9.

According to the Pythagorean theorem: the square of the hypotenuse is equal to the sum of the squares of the legs. Find the AC leg.

AC = √ (AB ^ 2 – BC ^ 2) = √ (18 * 18 – 9 * 9) = √243 = 9√3.

Answer: AC = 9√3.