In a triangle ABC, AC = BC = 5, AB = 8. Find tg A.

Let’s draw the height of the CH in the triangle ABC.

Since, by condition, AC = BC, then triangle ABC is isosceles, and therefore the height of CH is also the median of triangle ABC, which means AH = BH = AB / 2 = 8/2 = 4 m.

Consider a right-angled triangle ACH, and by the Pythagorean theorem we define the leg CH.

CH ^ 2 = AC ^ 2 – AH ^ 2 = 25 – 16 = 9.

CH = 3 cm.

Then tgA = CH / AH = 3/4.

Answer: tgA = 3/4.