In a triangle ABC, the sides b and c are fixe | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Using the Law of Cosines: $a^2 = b^2 + c^2 - 2bc \cos A$. Differentiating both sides with respect to $A$, we get: $2a \delta a = 2bc \sin A \delta

Vedclass · Accepted Answer

$\frac{\Delta \delta A}{2 R^2 \sin^2 A} 	imes 100$

Vedclass · Answer

(C) Using the Law of Cosines: $a^2 = b^2 + c^2 - 2bc \cos A$. Differentiating both sides with respect to $A$, we get: $2a \delta a = 2bc \sin A \delta A$. Thus, $\delta a = \frac{bc \sin A \delta A}{a}$. We know that the area of the triangle is $\Delta = \frac{1}{2} bc \sin A$, so $bc \sin A = 2\Delta$. Also, by the Sine Rule, $\frac{a}{\sin A} = 2R$, which implies $a = 2R \sin A$. Substituting these into the expression for $\delta a$: $\delta a = \frac{2\Delta \delta A}{2R \sin A} = \frac{\Delta \delta A}{R \sin A}$. The percentage error is $\frac{\delta a}{a} 	imes 100 = \frac{\Delta \delta A}{R \sin A \cdot 2R \sin A} 	imes 100 = \frac{\Delta \delta A}{2R^2 \sin^2 A} 	imes 100$.

In a $\triangle ABC$, the sides $b$ and $c$ are fixed. If there is an error of $\delta A$ in measuring angle $A$, then the percentage error in measuring the length of the side $a$ is:

Similar Questions

The total revenue in Rupees received from the sale of $x$ units of a product is given by $R(x) = 13x^2 + 26x + 15$. Find the marginal revenue when $x = 7$.

$A$ particle is moving on a straight line. The distance $S$ travelled in time $t$ is given by $S = at^2 + bt + 6$. If the particle comes to rest after $4 \text{ s}$ at a distance of $16 \text{ m}$ from the starting point,then the acceleration of the particle is:

The weight $W$ of a certain stock of fish is given by $W = nw,$ where $n$ is the size of the stock and $w$ is the average weight of a fish. If $n$ and $w$ change with time $t$ as $n = 2t^2 + 3$ and $w = t^2 - t + 2,$ then the rate of change of $W$ with respect to $t$ at $t = 1$ is

$A$ stone is dropped into a pond. Waves in the form of circles are generated and the radius of the outermost ripple increases at the rate of $5 \ cm/sec$. The rate at which the area increases after $2 \ seconds$ is:

$A$ circular plate of radius $5 \text{ cm}$ is heated. Due to expansion,its radius increases at the rate of $0.05 \text{ cm/s}$. The rate at which its area is increasing when the radius is $5.2 \text{ cm}$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module