Question

Given: △ABC, m∠B=90° AB=12, BC=16, BK ⊥ AC . Find: AC and BK. Please explain how to find out BK​

Answer 1

Answer:

Given: △ABC, m∠B=90° AB=12, BC=16, BK ⊥ AC . Find: AC and BK.

Given: △ABC, m∠B=90°

Find: AC and BK.

Short leg 90 degrees Long leg Hypotenuse

AB=12 90 BC=16 AC= ?

AK = ? 90 BK = ? AB=12

AC = SQRT (AB*AB + BC*BC) = 20 [right triangle; Pythagorean Theorem]

Similar triangles:[Note: In diagram, share two angles. Therefore share three angles]

BK / 16 = AB / AC

BK / 16 = 12 / 20

BK = (3/5)16

BK = 48/5

another answer let see this

AB^2+BC^2=AC^2

12^2+16^2=AC^2

144+256=AC^2

400=AC^2

20=AC

# be careful#

Answer 2

Answer: BK = 9.6

Step-by-step explanation: The equation of the line AC is y = (-3/4)x + 12. The line perpendicular to AC and passing through point B is y = (4/3)x. The point of intersection between BK amd AC is (144/25, 192/25). Those are the side lengths. Use Pythagorean theorem to find the hypotenuse.