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
Answers
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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