The length of the altitude to longest side of a triangle : 7.059 cm
Triangles are flat fields bounded by 3 intersecting sides and 3 angles
This side can be the same length or different.
Altitudes (h) are used to find the area of a triangle
[tex]\rm A=\dfrac{1}{2}\times base\times altitudes (h)[/tex]
If we know the lengths of all three sides, we can use Heron's formula to find out the area of the triangle
the Area:
[tex]\rm A=\sqrt{ (s (s-a) (s-b) (s-c))}[/tex]
where
s = semi-perimeter / half of the triangles perimeter
[tex]\rm s=\dfrac{a+b+c}{2}[/tex]
a, b, and c are side lengths
The lengths of the sides of a triangle: 15cm, 17cm, 8cm
Longest side: 17 cm
Then :
[tex]\rm s=\dfrac{a+b+c}{2}\\\\s=\dfrac{15+17+8}{2}\\\\s=20[/tex]
the Area:
[tex]\rm A=\sqrt{(s (s-a) (s-b) (s-c))}\\\\A=\sqrt{20 (20-15) (20-17) (20-8)}\\\\A=60[/tex]
The length of the altitude to the longest side (17 cm) can be searched from:
[tex]\rm A=\dfrac{1}{2}\times base\times h[/tex]
[tex]\rm 60=\frac{1}{2}\times 17\times h\\\\60=8.5\times h\\\\h=60:8.5\\\\h=\boxed{\bold{ 7,059}}[/tex]
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