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

Sagot :

Jerry787354

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#

akposevictor

ΔABC and ΔBKC are similar triangles, the missing measures are:

  • AC = 20 units
  • BK = 9.6 units.

What are Similar Triangles?

If two triangles are similar, their corresponding sides are proportional to each other.

When a segment of a right triangle intersects the hypotenuse, the triangles formed are similar to each other.

Thus, using Pythagorean Theorem:

AC = √(AB² + BC²)

Substitute

AC = √(12² + 16²)

AC = 20 units.

Find BK:

ΔABC ~ ΔBKC (similar right triangles)

Thus:

AB/BK = AC/BC

Substitute

12/Bk = 20/16

Cross multiply

BK = (16 × 12)/20

BK = 9.6

Therefore, ΔABC and ΔBKC are similar triangles, the missing measures are:

AC = 20 units

BK = 9.6 units.

Learn more about similar triangles on:

https://brainly.com/question/11899908

View image akposevictor
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