In triangle ABC, ∡A is a right angle, and m∡B = 45°. What is the length of BC? If your answer is not an integer, leave it in simplest radical form. (1 point) Responses 16 ft 16 ft 16 ft 16 Image with alt text: square root of 2 ft 16 ft 16 Image with alt text: square root of 3 ft 32 ft
To find the length of BC, we can use trigonometry. Since we know that ∠A is a right angle and ∠B = 45°, then ∠C = 180° - 90° - 45° = 45° as well.
We can now use the trigonometric ratios in a right triangle:
sin 45° = BC / AC
sin 45° = BC / AB
sin 45° = BC / BC (since AB = AC)
sin 45° = BC / BC
1 = BC / BC
So, the length of BC is BC = BC = 16 ft.
Therefore, the length of BC is 16 ft.