SOLUTION: the side of a triangle are 70 cm, 80cm and 90cm. compute the lenght of the altitude to the 80 cm side.

Question 468811: the side of a triangle are 70 cm, 80cm and 90cm. compute the lenght of the altitude to the 80 cm side.
Found 2 solutions by ccs2011, lwsshak3:
Answer by ccs2011(207) (Show Source): You can put this solution on YOUR website!
The altitude or height is always perpendicular to the opposite side.
Thus the altitude splits the triangle into 2 right triangles, of which the 2 hypotenuse sides are 70 and 90.
Let the vertices of one of the right triangles be ABC.
where AB = 70, BC = height
Using trig relationships:
sin(A) = height/70
=> height = 70*sin(A)
Now just find the measure of angle A by using the Law of Cosines:
90^2 = 70^2 + 80^2 - 2(70)(80)cos(A)
=> cos(A) = 0.2857
=> A = cos^-1(.2857) = 73.4
Substitute this value in for A to solve for height
=> height = 70*sin(73.4)
=> height = 67.1
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
the side of a triangle are 70 cm, 80cm and 90cm. compute the length of the altitude to the 80 cm side
...
Draw a triangle with sides 70 cm, 80 cm and 90 cm. From the apex opposite the 80 cm side drop a perpendicular to the 80 cm side which divides the side into two parts. Let x=one of the parts and (80-x) the other part. We now have two right triangles to work with. One right triangle has legs of x and the altitude(h) and hypotenuse of 90. The other right triangle has legs of (80-x) and the same altitude(h) and a hypotenuse of 70.
..
calculations:
h^2=70^2-(80-x)^2
h^2=90^2-x^2
..
70^2-(80-x)^2=90^2-x^2
4900-6400+160x-x^2=8100-x^2
160x=9600
x=60
h^2=90^2-x^2=8100-3600=4500
h=√4500=67.1 cm
ans:
Length of altitude to the 80 cm side=67.1 cm
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