Question

Triangle A B C is shown. Angle A B C is a right angle. An altitude is drawn from point B to point D on side A C to form a right angle. The length of A D is 5 and the length of B D is 12. What is the length of Line segment B C, rounded to the nearest tenth? 13. 0 units 28. 8 units 31. 2 units 33. 8 units.

Answer 1

Answer:

A NOT C

Step-by-step explanation:

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Answer 2

Applying the altitude theorem and the Pythagorean theorem, the length of line segment BC to the nearest tenth is: C. 31.2 units

Recall:

• Altitude theorem is given by, h = √(xy), where h is the altitude.

• Pythagorean theorem is given by, c = √(a²+b²), where c is the hypotenuse.

First find DC using the altitude theorem:

x = DC

y = 5 units

h = 12 units

12 = √(5×DC)

12² = 5(DC)

144/5 = DC

DC = 28.8

Considering right triangle BDC, use Pythagorean theorem to find BC:

BC = √(DC²+BD²)

• Substitute

BC = √(28.8²+12²)

BC = 31.2 units

In summary, applying the altitude theorem and the Pythagorean theorem, the length of line segment BC to the nearest tenth is: C. 31.2 units

Learn more about the altitude theorem on:

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