Question
In $\triangle A B C, \cos C=\frac{12}{13}$ and $B C=24$, then $A C=$ ?
✓
Answer
$\cos C=\frac{12}{13}$
.....(i) [Given]
In $\triangle ABC$,
Let $\angle A B C=90^{\circ}$
$\therefore \cos C =\frac{ BC }{ AC } \quad \ldots .$. (ii) [By definition]
$\therefore \frac{ BC }{ AC }=\frac{12}{13} \ldots \ldots[$ From (i) and (ii) $]$
$\therefore \frac{24}{ AC }=\frac{12}{13}$
$\therefore \frac{24 \times 13}{12}= AC$
$\therefore \frac{312}{12}= AC$
$\therefore AC =26$ units
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The A.P. in which 4th term is – 15 and 9th term is – 30. Find the sum of the first 10 numbers.
In the given figure, O is the centre of the circle and TP is the tangent to the circle from an external point T. If $\angle\text{PBT} = 30^\circ,$prove that
BA : AT = 2 : 1.
→BA : AT = 2 : 1.
Market value of shares and dividend declared by the two companies is given below. Face Value is same and it is Rs. 100 for both the shares. Investment in which company is more profitable?
(1) Company A - Rs. 132 , 12%
(2) Company B - Rs. 144, 16%
(1) Company A - Rs. 132 , 12%
(2) Company B - Rs. 144, 16%
Construct D A'BC' similar to D ABC such that AB:A'B = 5:7
Using prime factorization, find the HCF and LCM of:
96, 404
96, 404
Verify, whether points $P(6,-6), Q(3,-7)$ and $R(3,3)$ are collinear.
→If the equation $\left(1+m^2\right) x^2+2 m c x+\left(c^2-a^2\right)=0$ has equal roots, prove that $c^2=a^2\left(1+m^2\right)$.
→Find the value of $k$ for which given quadratic equation are real and equal roots.
$4 x^2-3 k x+1=0$
→$4 x^2-3 k x+1=0$
Solve the following simultaneous equations using Cramer’s rule.
4m + 6n = 54; 3m + 2n = 28
4m + 6n = 54; 3m + 2n = 28
For any positive integer n, prove that $n^3 - n$ is divisible by $6.$
→