Hypotenuse AB = 10 cm, BC = 8 cm. find tgA, tgB.

| June 11, 2021 | education

The word “hypotenuse” in the conditions of the task informs us that a right-angled triangle ABC is given with a right angle C. Thus, in a right-angled triangle ABC, the hypotenuse has a length of 10 cm, that is, AB = 10 cm, and one of the legs is BC = 8 cm.It is required to calculate the tangents of acute angles A and B.
In order to calculate the required values, we will use the definition of the tangent of an angle in a right-angled triangle. We have: tg∠A = ВС / АС and tg =В = АС / ВС. As you can see, in order to calculate the required tangents, you must first calculate the length of the AC leg.
Let’s use the Pythagorean formula, which for our triangle ABC has the form AB² = AC² + BC². Let’s rewrite this formula in the form AC² = AB² – BC² and calculate (add the unit of measurement cm to the result when we find the desired length of the leg AC): AC² = 10² – 8² = 100 – 64 = 36, whence AC = √ (36) = 6. Thus, AC = 6 cm.
Therefore, tg∠A = BC / AC = 8/6 = 4/3 and tg∠B = AC / BC = 6/8 = ¾.
Answer: tg∠A = 4/3; tg∠В = ¾.



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