Question

3. The acute angles of a right angled triangle are such that one
in seconds in sexagesimal system is equal to the other in
seconds in centesimal system. The acute angles are
81T 12511
(a)
(b)
662 331
4'4
TT TT
TO
(c) - T
3
TT
(d) none of these​

Answer 1

Given : The acute angles of a right angled triangle are such that one

in seconds in sexagesimal system is equal to the other in  seconds in centesimal system.

To Find : The acute angles are

Solution:

1 right angle in  centesimal system  = 100 deg

1 deg = 100 minutes

= 1 minutes = 100 Second

Hence 1  right angle = 100 * 100 * 100  = 10⁶ seconds

1 right angle in  sexagesimal system  = 90 deg

1 deg = 60 minutes

= 1 minutes = 60 Second

Hence 1  right angle = 90 * 60 * 60  =324 x 10³ seconds

Let say one acute angle =  A  deg

Then other acute angle = 90 - A  deg

A  10⁶  =  (90 - A ) 324 x 10³

=> 1000A  = (90 - A) 324

=> 1324A = 90 * 324

=> A = 22.02

  90 - A = 67.98

acute angles are  22.02°  and 67.98°  

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