Question

If in a right-angled triangle the hypotenuse is four times as long as the perpendicular drawn to it from opposite vertex, then find one of its acute angle.

Answer 1

See Fig. If x is length of perpendicular drawn to it from opposite vertex of a right-angled triangle, so, length of the diagonal is

AB = y₁ + y₂    ......(1)

From ∆OCB y₂, = xcot θ and from ∆OCA, y₁, = x tanθ. Putting the values in Eq. (1), we get

AB = x(tanθ + cotθ)   ......(2)

Since, length of hypotenuse = 4 (Length of perpendicular) therefore,