Question
In a right triangle ABC, angle B = 90°. If tan A = 3/4
and the length of the hypotenuse is 25 cm, find the area of the triangle.Solution
ATQ,
We have a right triangle with: tan A= 3/4, meaning the opposite side is 3x and the adjacent side is 4x. The hypotenuse is 25 cm.
Use the Pythagorean theorem: (3x)2 + (4x)2 = 252
Solve for x, which gives x=5. The sides of the triangle are: Opposite side = 3x=15 cm, Adjacent side = 4x=20 cm. The area is = (1/2) × 15 cm × 20 cm = 150 cm2
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