SOLUTION: How do you find the height of triangle whose base is 44cm and sides Are 38cm and 30cm?

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Question 491577: How do you find the height of triangle whose base is 44cm and sides Are 38cm and 30cm?
Found 2 solutions by cleomenius, lwsshak3:
Answer by cleomenius(959) About Me  (Show Source):
You can put this solution on YOUR website!
This will be done in two steps.
The first step is to find the area, we will use Heron's formula.
Area = sqrt%28s%28s+-+a%29%28s+-+b%29%28s-c%29%29
s = (a + b + c) / 2
112/2 = 56 = s
Area = sqrt%2856%2856+-+44%29%2856+-+38%29%2856-30%29%29
Area = sqrt%2856%2A12+%2A18%2A26%29 = 560.8 cm
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Now, we are able to use the formula area = 1/2b*h
1121.6 = 44 *h
h =25.5 cm.
Cleomenius.

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
How do you find the height of triangle whose base is 44cm and sides Are 38cm and 30cm?
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Draw a triangle with the apex labeled, A, the angle on the left, B and the the angle on the right, C. Draw a line from the apex down to where it intersects the base BC. Call this line h=height and label the point of intersection as D. The base is divided into two parts. Call the left part x, and the right part (44-x). We now have two right triangles to work with, ACD and ABD, and sides AB=38, AC=30, BC=44.
..
Using Pythagorean Theorem:
AB^2-h^2=x^2
38^2-h^2=x^2
h^2=38^2-x^2
..
AC^2-h^2=(44-x)^2
30^2-h^2=44^2-88x+x^2
sub h^2
30^2-38^2+x^2=44^2-88x+x^2
900-1444=1936-88x
-2480=-88x
x=2480/88=28.18
..
h^2=38^2-x^2=1444-28.18^2=649.79
h=√649.79=25.49 cm
ans:
Height of triangle=25.49 cm