In a right angled triangle, one acute angle is double the other. Then the hypotenuse is _______.

(A) Double the smallest side

(B) Thrice the smallest side

(C) 4 times the smallest side

(D) None

Asked by gpnkumar0 | 5th Aug, 2016, 06:31: PM

Expert Answer:

begin mathsize 16px style I n space a space r i g h t space a n g l e d space t r i a n g l e comma space o n e space a c u t e space a n g l e space i s space d o u b l e space t h e space o t h e r. space
T h e n space t h e space h y p o t e n u s e space i s space D o u b l e space t h e space s m a l l e s t space s i d e.
C o r r e c t space o p t i o n space i s space left parenthesis A right parenthesis.
I n space t r i a n g l e space A B C comma space a n g l e space B space i s space r i g h t space a n g l e.
L e t space angle space B A C equals x
T h e n comma space angle A C B equals 2 x
N o w comma space i n space t r i a n g l e space A B C comma
x plus 2 x plus 90 equals 180 degree
3 x equals 90
x equals 30
angle B A C equals 30 degree
rightwards double arrow angle A C B equals 2 x equals 60 degree
S i d e space o p p o s i t e space t o space t h e space s m a l e s t space a n g l e space i s space t h e space s m a l e s t
H e n c e comma space s i d e space B C space i s space t h e space s m a l l e s t
N o w comma space cos space 2 x equals fraction numerator B C over denominator A C end fraction
rightwards double arrow cos space 60 degree equals fraction numerator B C over denominator A C end fraction
rightwards double arrow 1 half equals fraction numerator B C over denominator A C end fraction
rightwards double arrow A C equals 2 B C end style

Answered by Rashmi Khot | 7th Aug, 2016, 10:15: AM