n triangle ABC, right angled at B, if tanA = 1√3 . Find the values of:

In triangle ABC, right angled at B, we are given that tanA = 1/√3.

Step 1: Recall that in a right triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

Step 2: Since we are given that tanA = 1/√3, we can conclude that the length of the side opposite angle A is 1 and the length of the side adjacent to angle A is √3.

Step 3: Using the Pythagorean theorem, we can find the length of the hypotenuse of triangle ABC. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Step 4: Let's denote the length of the hypotenuse as c, the length of the side opposite angle A as a, and the length of the side adjacent to angle A as b. Applying the Pythagorean theorem, we have c^2 = a^2 + b^2.

Step 5: Substituting the values we found earlier, we have c^2 = 1^2 + (√3)^2 = 1 + 3 = 4.

Step 6: Taking the square root of both sides, we find c = 2.

Step 7: Therefore, the length of the hypotenuse of triangle ABC is 2.