Two Sides of a Triangle Are $2 \mathrm {~m}$ And $3 \mathrm {~m}$

question 58

Multiple Choice

Two sides of a triangle are $2 \mathrm {~m}$ and $3 \mathrm {~m}$ in length and the angle between them is increasing at a rate of $0.06 \mathrm { rad } / \mathrm { s }$ . Find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is $\frac { \pi } { 3 }$ .

• A) \(1.145 \mathrm {~m} ^ { 2 } / \mathrm { s }\)
• B) \(- 0.955 \mathrm {~m} ^ { 2 } / \mathrm { s }\)
• C) \(0.090 \mathrm {~m} ^ { 2 } / \mathrm { s }\)
• D) \(5.045 \mathrm {~m} ^ { 2 } / \mathrm { s }\)
• E) \(- 1.955 \mathrm {~m} ^ { 2 } / \mathrm { s }\)

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