Answer:
h = 7.1 cm
Step-by-step explanation:
To find the height of the triangle, we can first find the area of the triangle using the Heron's formula:
[tex]S = \sqrt{p(p-a)(p-b)(p-c)}[/tex]
Where a, b and c are the sides of the triangle and p is the semi perimeter of the triangle:
[tex]p = \frac{a+b+c}{2} = \frac{15 + 8 + 17 }{2} = 20\ cm[/tex]
So the area of the triangle is:
[tex]S = \sqrt{20(20-15)(20-8)(20-17)}[/tex]
[tex]S = 60\ cm^2[/tex]
Now, to find the height, we can use the following equation for the area of the triangle:
[tex]S = base * height/2[/tex]
The height draw in the figure is relative to the side of 17 cm, so this side is the value of base used in the formula. So we have that:
[tex]60 = 17 * h/2[/tex]
[tex]h = 120/17[/tex]
[tex]h = 7.06\ cm[/tex]
Rounding to the nearest tenth, we have h = 7.1 cm
