1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Svetllana [295]
3 years ago
9

In triangle △ABC, ∠ABC=90°, BH is an altitude. Find the missing lengths. AC=5 and BH=2, find AH and CH.

Mathematics
1 answer:
Yakvenalex [24]3 years ago
3 0

Answer:

  AH = 1 or 4

  CH = 4 or 1

Step-by-step explanation:

An altitude divides a right triangle into similar triangles. That means the sides are in proportion, so ...

  AH/BH = BH/CH

  AH·CH = BH²

The problem statement tells us AH + CH = AC = 5, so we can write

  AH·(5 -AH) = BH²

  AH·(5 -AH) = 2² = 4

This gives us the quadratic ...

  AH² -5AH +4 = 0 . . . . in standard form

  (AH -4)(AH -1) = 0 . . . . factored

This equation has solutions AH = 1 or 4, the values of AH that make the factors be zero. Then CH = 5-AH = 4 or 1.

You might be interested in
Need help ASAP !!!!<br> Solve for the missing side. Round answer to two decimal places (like 7.93).
Thepotemich [5.8K]
10.44yd
a^2 + b^2 = c^2
3^2 + 10^2 = c^2
109 = c^2
C (Hypotenuse) ≈ 10.44
3 0
3 years ago
keisha spent 45 minutes at soccer practice on Monday and n minutes on Tuesday. Write an experession that repersents the number o
levacccp [35]

Answer:

45+n

Step-by-step explanation:


6 0
3 years ago
Read 2 more answers
Paige used three congruent triangles<br> and a semicircle to design the tulip logo<br> shown.
Dennis_Churaev [7]
I think it’s the triangle logo
7 0
3 years ago
Find two numbers whose sum is 28 and whose difference is 13
andrey2020 [161]
I could be wrong but 20.5 and 7.5
7 0
2 years ago
What is - 8/41 as a repeating decimal?
ss7ja [257]

Answer:

-0.(19512) = -19512/99999

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Other questions:
  • A certain ore is 31.8% nickel by mass. How many kilograms of this ore would you need to dig up to have 25.0 g of nickel?
    9·1 answer
  • What is the value of x in this equation?<br><br> 2x + 2 = -5
    9·2 answers
  • In the diagram below, DE is parallel to XY . What is the value of x
    12·1 answer
  • Andy and Jacob work as technicians in a laboratory where gemstones are tested and certified. Andy has already tested 30 gemstone
    13·1 answer
  • Write the equation of a line parallel to y=3
    10·2 answers
  • OMG HELP!!!!!!!!!!!!!!!!!!!!!!!!!! ME!!!!!!!!!!!!!!!!!!
    10·1 answer
  • F. ALGEBRA Find x.<br> a. 25.6<br> b. 22.5<br> c. 38<br> d. 40
    7·1 answer
  • HELP PLEASE I NEED THIS QUESTION
    5·1 answer
  • (3 x 7) + (3 x 5) is the same as
    11·1 answer
  • Someone pls anwser this.​
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!