An archer shoots at a target which is at a height of 6 m and at a line of sight distance of 12 m from the bow. Which of the following angles of shooting the arrow gives him a fair chance of hitting the target taking gravity into account?

Concept:

The trigonometry formulas are given below:

\(sin\theta=\frac{opposite}{hypotenuse}\)

\(cos\theta=\frac{base}{hypotenuse}\)

\(tan\theta=\frac{opposite}{base}\)

Explanation:

The base is 12 m and the height of the target is 6 m. 

Considering the trigonometry relation:

\(sin\theta=\frac{opposite}{hypotenuse}\)

\(sin\theta=\frac{6m}{12m}\)

\(sin\theta=\frac12\)

\(\theta=sin^{-1}(\frac12)\)

\(\theta=30^o\)

Due to the effect of gravity, the target should be aimed a little higher than 30^o. So, the angle aimed will be : 32^o.