Question

(b) 30°
(d) none of these

10. In a right angled triangle, the hypotenuse is four times as

long as the perpendicular drawn to it from the opposite
vertex. One of the acute angle is
(a) 15°
(c) 45


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Answer 1

Answer:

Step-by-step explanation: Let L be the hypotenuse with sides A and B with the perpendicular l.

A^2 + B^2 = L^2  

l^2 + x^2 = A^2    and l^2 + (L- x)^2 = B^2 where the hypotenuse is divided into L and L -x by the perpendicular

You can substitute L = 4 l and combine equations to get

18 l^2 + 2 x^2 - 8 x l = A^2 + B^2 = L^2 = 16 l^2

or l^2 - 4 x l + x^2 = 0

Solve the quadratic and l = 3.732 x

tan theta = l / x = 3.732 giving theta = 75 deg

So the opposite angle must be 15 deg.