Question

In ΔABC, ∡A is a right angle, and m∡B = 45°. What is the length of BC? If the answer is not an integer, leave it in simplest radical form. The diagram is not drawn to scale.

Answer 1

BC² = 11² + 11²

BC² = 121 + 121

BC² = 242

BC = √242

BC = 11√2

Answer: 11√2

Answer 2

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,

$\frac{sin B}{AC}=\frac{sin A}{BC}$

$\implies BC\times sin B = AC\times sin A$   ( By cross multiplication )

$\implies BC = \frac{AC\times sin A}{sin B}$

By substituting the values,

$BC=\frac{11\times sin 90^{\circ}}{sin 45^{\circ}}$

$=\frac{11}{\frac{1}{\sqrt{2}}}$

$=11\sqrt{2}$

Hence, the length of BC is 11√2 ft.