Question

One side of a right triangle is known to be 12 cm long and the opposite angle is measured as 30°, with a possible error of ±1°. Use differentials to estimate the error in computing the length of the hypotenuse. (Round your answer to two decimal places.)

Answer 1

Answer:

estimated error=±0.725

Step-by-step explanation:

Side of the triangle= 12cm

Opposite of triangle x= 30

h= hypotenose side

Error= =±1

From trigonometry

Sin(x)=opposite/hypotenose

hypotenose=opposite/sin(x)

h=12/sin(x)

h=12Csc(x)

dh=-12Csc(x)Cot(x) dx...............eqn(1)

dx is the possible error in angle measurements

So we need to convert to radius

dx=±1°× (π/180)

=±1°(π/180)

Substitute x and dx into equation (1)

dh= - 12Csc30°Cot30°×[±(π/180)]

= -12(2)(√3)(±(π/180)

==±0.725

Therefore, estimated error=±0.725