In a triangle ABC, AC = BC = 5, AB = 8. Find tg A.
June 25, 2021 | education
| 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.
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