In triangle △ABC, ∠ABC=90°, BH is an altitude. Find the missing lengths. AB=4 and BC=3, Find AH, CH and BH.
1 answer:
Answer:
- AH = 3.2
- CH = 1.8
- BH = 2.4
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
You might be interested in
Answer:
The area of the second enlargement is 1,944 square inches
The area of the second enlargement is (3 squared) squared times the original area.
The ratio of the area of the first enlargement to the area of the original equals the square of the scale factor
Step-by-step explanation:
<u><em>Verify each statement</em></u>
1) The area of the first enlargement is 72 square inches.
The statement is false
Because
we know that
The original dimensions of the rectangle are
length 6 inches and width 4 inches
so
First enlargement
Multiply the original dimensions by a scale factor of 3
The area of the first enlargement is
2) The area of the second enlargement is 1,944 square inches
The statement is true
Multiply the dimensions of the first enlargement by a scale factor of 3
The area of the second enlargement is
3) The area of the second enlargement is (3 squared) squared times the original area.
The statement is true
Because
The original area is 24 square inches
4) The area of the second enlargement is 3 times the area of the first enlargement
The statement is false
Because
so
5) The ratio of the area of the first enlargement to the area of the original equals the square of the scale factor
The statement is true
Because
The square of the scale factor is 3^2=9
and the ratio is equal to