Question

Please I need help on these 2 thank you so much

Answer 1

Given the triangle below,

To find GR which is the adjacent of the right-angled triangle above,

Using SOHCAHTOA

`\begin{gathered} \cos \theta=(Adj)/(Hyp) \\ \text{Where} \\ \text{Hyp}=18\sqrt[]{3} \\ \text{Adj}=GR \\ \theta=30^0 \end{gathered}`

Substituting the values into the formula above,

`\begin{gathered} \cos 30^0=\frac{GR}{18\sqrt[]{3}} \\ \text{Where} \\ \cos 30^0=\frac{\sqrt[]{3}}{2} \\ \frac{\sqrt[]{3}}{2}=\frac{GR}{18\sqrt[]{3}} \end{gathered}`

Crossmultiply to find GR,

`\begin{gathered} \sqrt[]{3}*18\sqrt[]{3}=2* GR \\ 18*3=2GR \\ \text{Divide both sides by 2} \\ (2GR)/(2)=(18*3)/(2) \\ GR=27\text{units} \end{gathered}`

Hence, the third option is the answer.