Download App

Sine And Cosine Formulae And Their Applications — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsSine And Cosine Formulae And Their Applications1 Mark
Question
In a $\triangle\text{ABC},$ if a = 8, b = 10, c = 12 and $\text{C}=\lambda\text{A},$ find the value of $\lambda.$
✓

Answer

Using cosine rule, we have
$\cos\text{A}=\frac{\text{b}^2+\text{c}^2-\text{a}^2}{2\text{bc}}$
$\Rightarrow\cos\text{A}=\frac{10^2+12^2-8^2}{2\times10\times12}$
$\Rightarrow\cos\text{A}=\frac{100+144-64}{240}$
$\Rightarrow\cos\text{A}=\frac{180}{240}=\frac{3}{4}...(1)$
Now, using sine rule, we have
$\Rightarrow\frac{\text{a}}{\sin\text{A}}=\frac{\text{c}}{\sin\text{C}}$
$\Rightarrow\frac{8}{\sin\text{A}}=\frac{12}{\sin\lambda\text{A}}$
$\Rightarrow\sin\lambda\text{A}=\frac{3}{2}\sin\text{A}$
$\Rightarrow\sin\lambda\text{A}=2\times\frac{3}{4}\sin\text{A}$
$\Rightarrow\sin\lambda\text{A}=2\sin\text{A}\cos\text{A}$ [Using (1)]
$\Rightarrow\sin\lambda\text{A}=\sin2\text{A}$
$\Rightarrow\lambda=2$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the following Question.(1 Marks)" from Sine And Cosine Formulae And Their Applications→Sine And Cosine Formulae And Their Applications — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

State the quadrant in which 6 lies if : tan θ < 0 and sec θ > 0
→
If, $S_1$ is the sum of an arithmetic progression of $'n\ '$ odd number of terms and $S_2$ the sum of the terms of the series in odd places, then $\frac{\text{S}_1}{\text{S}_2}=$
→
Write the $50^{th}$​​​​​​​ term of the series $2 + 3 + 6 + 11 + 18 + ....$
→
If the first, second and last term of an A.P are a, b and 2 a respectively, then its sum is:
  1. $\frac{2\text{n}}{\text{n}+1}$
  2. $\frac{\text{n}}{\text{n}+1}$
  3. $\frac{\text{n}+1}{2\text{n}}$
  4. $\frac{\text{n}+1}{\text{n}}$
→
Find the value of : $\omega^{18}$
→
Evaluate the following limits : $\lim _{x \rightarrow-3}\left[\frac{x+3}{x^2+4 x+3}\right]$
→
Express the following exponential equations in logarithmic form:

$9^{\frac{3}{2}}=27$

→
Check the validity of the following statements:
r: 60 is a multiple of 3 or 5.
→
Write down the power set of A = {1, 2, 3}.
→
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following: (A ∪ B) = (A – B) ∪ (A ∩ B) ∪ (B – A)
→