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°.(a) use differentials to estimate the error in computing the length of the hypotenuse. (round your answer to two decimal ± cm(b) what is the percentage error? (round your answer to the nearest integer.)± %

a) ±0.73

b) ±3%

Step-by-step explanation:

One side of the right angle triangle is 12cm

The opposite angle(x) is 30 degree

Possible error = ±1degree

a) Let the hypotenus= h

h/12 = cosecx

h = 12cosecx

Differentiate h with respect to x

dh= -12cosecxcotcdx

The possible error in the angle measurement is dx

dx= ±1degree

Convert degree to radians

dx = ±1*π/180

dx = ± π/180

Put x and dx into dh

dh = -12cosec30cot30(±π/180)

= -12(2)(√3)(±π/180)

= -24√3(±π/180)

= ±24π√3/180

= ±0.73

b) To find the percentage error, recall that

dh = 12cosecx

dh = 12cosec30

dh = 12(2)

= 24

Percentage error =

(change in value/initial value) 100

Percentage error = (dh/h)100

= (±0.73/24)100

= ±0.030*100

= ±3%

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step-by-step explanation: