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What is the length of Line Segment BC?
15 units
9 units
11 units
16 units
(Image: Triangle A B C is shown. Angle A C B is a right angle. An altitude is drawn from point C to a point on side A B to form a right angle. The length of A B is 17 and the length of A C is 8.)
To find the length of line segment BC in triangle ABC, we can use the Pythagorean theorem since angle ACB is a right angle.
Given:
– AB = 17 units
– AC = 8 units
To find BC, we need to find the length of the third side. We can use the relation from the Pythagorean theorem:
[ AB^2 = AC^2 + BC^2 ]
Substitute the known values:
[ 17^2 = 8^2 + BC^2 ]
[ 289 = 64 + BC^2 ]
[ BC^2 = 289 – 64 ]
[ BC^2 = 225 ]
Now, take the square root:
[ BC = sqrt{225} ]
[ BC = 15 text{ units} ]
So, the length of line segment BC is 15 units.