Given:
In ΔABC, the measure of ∠C=90°, the measure of ∠A=49°, and BC = 5.1 feet.
We need to determine the length of AB
Length of AB:
The image of the triangle ABC is attached below.
Using the figure, we shall determine the length of AB by the trigonometric ratio.
Thus, we have;
[tex]sin \ \theta=\frac{opp}{hyp}[/tex]
where [tex]\theta=49^{\circ}[/tex], [tex]opp=BC[/tex] and [tex]hyp=AB[/tex]
Thus, we have;
[tex]sin \ 49^{\circ}=\frac{BC}{AB}[/tex]
Substituting BC = 5.1, we get;
[tex]0.7547=\frac{5.1}{AB}[/tex]
Simplifying, we have;
[tex]AB=\frac{5.1}{0.7547}[/tex]
Dividing, we get;
[tex]AB=6.7577[/tex]
Rounding off to the nearest tenth, we get;
[tex]AB=7.8[/tex]
Thus, the length of AB is 7.8 feet.
