# Calculus

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The measurement of one side of a right triangle is found to be 9.5 inches, and the angle opposite that side is 26°45' with a possible error of 1.5'.

Approximate the percent error in computing the area of the triangle.

• Calculus -

Area of right triangle
=(1/2)L*(L)cot(θ)
=(1/2)L²cot(θ)
L=9.5,
θ=26°45' ± 1.5'
If you have not done calculus yet, calculate the area based on the given θ, then calculate the largest and smallest possible value of θ to give the higher and lower limits.

If you have done calculus, set
A(θ)=L²cot(θ) and differentiate with respect to θ to get e=A'(θ). Multiply e by the error in θ to give the error in area.
I get ±0.000516 sq.in. using both methods.

• Calculus -

The calculated error should therefore read:
"I get ±0.097 sq.in. using both methods."

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