One side of a right triangle is known to be 9 cm long and the opposite angle is measured as 30°, with a possible error of ±1°. (a) use differentials to estimate the error in computing the length of the hypotenuse. (round your answer to two decimal places.)
Hypotenuse, L= 9 cosec x
dL = 9 Cosec x *( cot x) dx
dx( error in angle)=1 deg = Pi/180 radians
dL,(error in Length of Hypotenuse at x= 30 deg)= 9* cosec 30* cot 30* PI/180
= 9*2*4*Pi/180
= 2/5 * Pi/180
It indicates 1% error in angle measurement result in 40% error in Length measurement
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