Fine the missing side lengths for x and y
2 answers:
9514 1404 393
Answer:
Step-by-step explanation:
The side ratios of a 30°-60°-90° triangle are ...
1 : √3 : 2
In your triangle, they are ...
x : 4 : y
In order to get these values, we need to multiply the reduced ratio by 4/√3 = (4√3)/3. Then we have ...
x : 4 : y = (4√3)/3 : 4 : (8√3)/3
and we can see that ...
- x = (4√3)/3
- y = (8√3)/3
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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
