In the rectangle ABC, the hypotenuse AB is 13 cm. Find the BC leg if tgB = 2.4.
| March 5, 2021 | education
1. By the condition of the problem, the tangent ∠В = 2.4.
The tangent ∠B is the quotient of dividing the AC leg, located opposite this angle, by the BC leg, which is the side of this corner, that is, adjacent to it.
Therefore, AC / BC = 2.4. AC = 2.4 BC.
2. Calculate the length of the BC leg using the Pythagorean theorem:
AC² + BC² = AB².
3. Replace AC in this expression with 2.4BC:
(2.4BC) ² + BC² = 169.
5.76BC² + BC² = 169.
6.76BC² = 169.
BC² = 25.
BC = √25 = 5 centimeters.
Answer: the length of the BC leg is 5 centimeters.
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