Question

# Find the value of $5\sin {30^ \circ } + 3\tan {45^ \circ }.$

Hint: In order to solve this type of question, firstly we have to substitute the value of $\sin {30^ \circ }$ and $\tan {45^ \circ }$ in the given equation. As we know that $\sin {30^ \circ } = \dfrac{1}{2}$ and $\tan {45^ \circ } = 1$.

$5\sin {30^ \circ } + 3\tan {45^ \circ } - - - - \left( 1 \right)$
Now, putting the value of $\sin {30^ \circ }$ and $\tan {45^ \circ }$ in equation (1) , we get
$5\sin {30^ \circ } + 3\tan 45$
We know that $\sin {30^ \circ } = \dfrac{1}{2}$and $\tan {45^ \circ } = 1$
$5 \times \dfrac{1}{2} + 3 \times 1$
Or $\dfrac{5}{2} + 3$
Or $\dfrac{{5 + 6}}{2}$
Or $\dfrac{{11}}{2}$ is our desired answer.
Note: Whenever we face such a type of question the key concept is that we should write what is given to us, like we did. Then we have to substitute the value of $\sin {30^ \circ }$and $\tan {45^ \circ }$in the given question and we will get our desired answer.