Question

Hi how are you I need help with this question.

Answer 1

Hello

Question one requires us to find the value of the angle

Using trigonometric ratios

SOHCAHTOA

`\begin{gathered} \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \\ \text{opposite}=8 \\ \text{adjacent}=10 \\ \tan \theta=(8)/(10) \\ \tan \theta=0.8 \\ \theta=\tan ^(-1)0.8 \\ \theta=38.66\approx38.7^0 \end{gathered}`

For question b, we can use trigonometric ratio to find the value of the missing side or use pythagoran's theorem

I would use pythagoran's theorem here because we would arriave at our answer faster

`\begin{gathered} x^2=y^2+z^2 \\ x^2=8^2+10^2 \\ x^2=64+100 \\ x^2=164 \\ \text{take the square root of both sides} \\ x=\sqrt[]{164} \\ x=12.81\approx12.8 \end{gathered}`

From the calculations above, the value of the angle is 38.7 degree and the missing side is 12.8 units