Answer:
The length of BC is 11√2 ft.
Step-by-step explanation:
Given,
A right angled triangle ABC,
In which,
AC = 11 ft ( By diagram ),
∠A = 90°,
∠B = 45°,
By the law of sine,
[tex]\frac{sin B}{AC}=\frac{sin A}{BC}[/tex]
[tex]\implies BC\times sin B = AC\times sin A[/tex] ( By cross multiplication )
[tex]\implies BC = \frac{AC\times sin A}{sin B}[/tex]
By substituting the values,
[tex]BC=\frac{11\times sin 90^{\circ}}{sin 45^{\circ}}[/tex]
[tex]=\frac{11}{\frac{1}{\sqrt{2}}}[/tex]
[tex]=11\sqrt{2}[/tex]
Hence, the length of BC is 11√2 ft.
