To answer this question we will use the trigonometric function cosine.
Recall that in a right triangle:
[tex]\cos\theta=\frac{AdjacentLeg}{Hypotenuse}.[/tex]
Using the given diagram we get that:
[tex]\cos78^{\circ}=\frac{x}{26}.[/tex]
Multiplying the above result by 26 we get:
[tex]\begin{gathered} 26\times\cos78^{\circ}=26\times\frac{x}{26}, \\ 26\cos78^{\circ}=x. \end{gathered}[/tex]
Therefore:
[tex]x\approx5.41.[/tex]
Answer:
[tex]x=5.41.[/tex]
