At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
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#
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
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.