Question

Find x in these 45°-45°-90° triangles. 24 X 1 2 3 4 5 6 7 8 9 97

Answer 1

Use the Cosine ratio from the figure given:

`\cos 45^(\circ)=\frac{x}{\sqrt[]{24}}`

Cross multiply:

`x=\sqrt[]{24}\cos 45^(\circ)`

Recall that the value of cos 45 is :

`\cos 45^(\circ)=\frac{1}{\sqrt[]{2}}`

Substitute this value into the equation above to solve for x:

`\begin{gathered} x=\sqrt[]{24}(\frac{1}{\sqrt[]{2}}) \\ x=\sqrt[]{(24)/(2)} \\ x=\sqrt[]{12}=\sqrt[]{4*3} \\ x=\sqrt[]{4}*\sqrt[]{3} \\ x=2\sqrt[]{3} \end{gathered}`