In a $$ riangle ABC $$ right-angled at $$ B $$, if $$ BC = 4 \, ext{cm} $$ and $$ \angle C = 60^\circ $$, then the length of $$ AC $$ is:

Question

In a $$ 	riangle ABC $$ right-angled at $$ B $$, if $$ BC = 4 \, 	ext{cm} $$ and $$ \angle C = 60^\circ $$, then the length of $$ AC $$ is:

Accepted Answer

In a right-angled triangle, the cosine of an angle is given by:  
$$
\cos(	heta) = \frac{	ext{Adjacent Side}}{	ext{Hypotenuse}}
$$  
Here, $$ BC = 4 \, 	ext{cm} $$, $$ AC = x $$, and $$ \angle C = 60^\circ $$. Using the formula:  
$$
\cos(60^\circ) = \frac{{1}}{2}
$$  
Substitute the values:  
$$
\frac{{1}}{2} = \frac{4}{x}
$$  
Cross-multiply to solve for $$ x $$:  
$$
x = 8
$$

Thus, the length of $$ AC $$ is **$$ 8 \, 	ext{cm} $$**.

Answer

Answer

Answer