Answer:
Step-by-step explanation:
Please see the picture attached also.
In triangle ABC, since two legs are given using Pythagorus theorem
we get AC = 5
We have triangle ABC and CHB having congruent angles
Hence they are similar and sides are proportional
[tex]\frac{BH}{BC} =\frac{4}{5} \\BH=3(\frac{4}{5})\\BH=2.4[/tex]
In right angled triangle CHB, we have two sides.
Hence third side
CH =[tex]\sqrt{3^2-2.4^2} \\=1.8[/tex]
Now AH = AC-CH
= 5-1.8
=3.2
Answer:
AH = 3.2
CH = 1.8
BH = 2.4
I hope this helps! Brainliest please!
Step-by-step explanation:
It can be convenient to compute the length of the hypotenuse of this triangle (AC). The Pythagorean theorem tells you ...
AC^2 = AB^2 + CB^2
AC^2 = 4^2 + 3^2 = 16 + 9 = 25
AC = √25 = 5
The altitude divides ∆ABC into similar triangles ∆AHB and ∆BHC. The scale factor for ∆AHB is ...
scale factor ∆ABC to ∆AHB = AB/AC = 4/5 = 0.8
And the scale factor to ∆BHC is ...
scale factor ∆ABC to ∆BHC = BC/AC = 3/5 = 0.6
Then the side AH is 0.8·AB = 0.8·4 = 3.2
And the side CH is 0.6·BC = 0.6·3 = 1.8
These two side lengths should add to the length AC = 5, and they do.
The remaining side BH can be found from either scale factor:
BH = AB·0.6 = BC·0.8 = 4·0.6 = 3·0.8 = 2.4
_____
The sides of interest are ...
AH = 3.2
CH = 1.8
BH = 2.4
