Question
In triangle ABC, ∡A is a right angle, and m∡B = 45°.
A right triangle A B C is shown. Angle A is marked with a small square, side B C is opposite angle A, and vertical leg A C is labeled 16 feet.
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
16square root of 2 ft
16 Image with alt text: square root of 2 ft
16square root of 3 ft
16 Image with alt text: square root of 3 ft
32 ft
32 ft
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Since angle B is 45 degrees and angle A is a right angle, this means that angle C must be 45 degrees as well because the sum of the angles in a triangle is always 180 degrees.
We can use the properties of a right triangle to find the length of BC. In a right triangle, the side opposite the right angle is called the hypotenuse. Since AC is 16 feet, this means that BC is also the hypotenuse.
Using the Pythagorean theorem, we can find the length of BC. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let x be the length of BC.
x^2 = 16^2 + 16^2 (applying the Pythagorean theorem)
x^2 = 256 + 256
x^2 = 512
x = √512 (taking the square root of both sides)
x = 16√2 (simplifying the square root)
Therefore, the length of BC is 16√2 feet.