Question

What will be the estimate error made in calculating the area of the triangle ABC in which the sides a and b are measured accurately as 25 cm and 16 cm, while the angle C is measured as 60° but (1/2)° in error?

(a) 55/63 sq cm

(b) 53/63 sq cm

(c) 55/67 sq cm

(d) Data not sufficient

This question was addressed to me by my school teacher while I was bunking the class.

I want to ask this question from Application of Derivative for Error Determination in chapter Application of Derivatives of Mathematics – Class 12

Answer 1

Correct option is (a) 55/63 sq cm

To explain: Let, y be the area of the triangle ABC.

Then, y = ½(ab)(sinC) where a and b are constants.

Now, dy = dy/dC * dC = ½(ab)(sinC) dC

Now, by problem, a = 25, b = 16, C = 60° and δC = (1/2)° = π/180 * ½ radian

Therefore, dy = 1/2 * 25 * 16 * cos60° * π/180 * ½ sq cm

=> dy = 25 * 8 * ½ * 22/7 * 1/180 * ½ sq cm

= 55/63 sq cm