In triangle ABC, given angle A = 90 degrees, angle B = 60 degrees, AC = 9 Find the other sides and area of the triangle

Based on the condition, we can say that our triangle is rectangular.

Let us find out what the hypotenuse will equal in it, if from the condition of our task we know for sure that the AC leg, whose length is 9, is opposite an angle of 60 °:

sin 60 ° = √3 / 2;

BC = 9: √3 / 2 = 18 / √3.

Let’s find out what the length of the other leg will be equal to in this case:

√ ((18 / √3) ^ 2 – 9 ^ 2) = √ (108 – 81) = √27 = 3√3.

Let’s determine what the area will be equal to:

9 * 3√3 * 1/2 = 13.5√3.

Answer: BC = 18 / √3; AB = 3√3, and S = 13.5√3.