AP EAMCET · Maths · Properties of Triangles

In $\triangle A B C$, if $a=5, b=4$ and $\cos (A-B)=\frac{31}{32}$, then $c=$

A $8$
B $\sqrt{41}$
C $6$
D $\sqrt{24}$

Verified Solution

Answer & Solution

Correct Answer

(C) $6$

Step-by-step Solution

Detailed explanation

No Solution

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

If $(\alpha, \beta)$ is the external centre of similitude of the circles $x^2+y^2=3$ and $x^2+y^2-2 x+4 y+4=0$, then $\frac{\beta}{\alpha}=$

AP EAMCET 2025 Medium
The value of $k$, if $(1,2),(k,-1)$ are conjugate points with respect to the ellipse $2 x^2+3 y^2=6$ is

AP EAMCET 2007 Hard
$\mathrm{S}=\{\mathrm{z} \in \mathrm{C} /|\mathrm{z}-1+\mathrm{i}|=1\}$ represents

AP EAMCET 2023 Medium
Let $z_1, z_2$ be two complex numbers such that $\bar{z}_1-i \bar{z}_2=0$ and $\arg \left(z_1 z_2\right)=\frac{3 \pi}{4}$, then $\arg \left(z_1\right)=$

AP EAMCET 2020 Easy
The radius and the height of a right circular solid cone are measured as 7 feet each. If there is an error of 0.002 ft for every feet in measuring them, then the error in the total surface area of the cone (in sq. ft ) is

AP EAMCET 2025 Medium
Define $f: C \rightarrow \mathrm{R}$ by $f(z)=|z|, \forall z \in C$. Then, which of the following is false ?

AP EAMCET 2021 Medium

Explore more questions on app

From AP EAMCET

For $1 \leq r \leq n, \frac{1}{r + 1} \{{}^{n}{P_{r + 1}} - {}^{(n - 1)}P_{r + 1}\}$ is equal to

AP EAMCET 2021 Medium
If a focal chord of the parabola $y^2=4 x$ makes an angle $45^{\circ}$ with positive $\mathrm{X}$-axis, then the slopes of the normals drawn at the ends of the focal chord will satisfy the equation

AP EAMCET 2018 Medium
If four dice are thrown simultaneously, then the probability that none of the dice shows the number 1 on its face, is

AP EAMCET 2023 Easy
Match the following.

$\begin{array}{llll}A & B & C & D\end{array}$

AP EAMCET 2014 Medium
A light wave has a frequency of $4 \times 10^{14} \mathrm{~Hz}$ and a wavelength of $5 \times 10^{-7} \mathrm{~m}$ in a medium. The refractive index of the medium is

AP EAMCET 2020 Easy
What is the ratio of kinetic energies of 3 g of hydrogen and 4 g of oxygen at a certain temperature?

AP EAMCET 2024 Easy

Explore more questions on app

In \(\triangle A B C\), if \(a=5, b=4\) and \(\cos (A-B)=\frac{31}{32}\), then \(c=\)

Answer & Solution

Step-by-step Solution

See the Complete Solution