Gary, $G$, can just see the top of a radio mast, $R$, over a wall $W$. Gary is $15\,\mathrm{m}$ from the wall. The wall is $45\,\mathrm{m}$ from the radio mast. The wall is $2.7\,\mathrm{m}$ high. Calculate the height of the radio mast, marked $h$ on the diagram.
How would you found the missing length $h$? I was thinking of doing Tan, Cos and Sin but I'm not that sure and I also had the idea of doing $15$ $+$ $45$ $=$ $60$ and then $2.7$ something. I know the answer is $10.79$ but I have no idea how that was worked out. Thanks.
The smallest triangle is similar to the larger triangle, so we can use ratios to solve for the height $h$ of the larger triangle. $$\dfrac {\text{(height)}_\text{large}}{\text{(base)}_{\text{large}}} = \dfrac {\text{(height)}_{\text{small}}}{\text{(base)}_{\text{small}}}$$
$$\dfrac{h}{15+45} = \dfrac{2.7}{15}$$