Answer:
The length of AC should be between 5 inches and 25 inches
Step-by-step explanation:
Jose in this problem draws a triangle, ABC.
We know the length of two sides of the triangle:
AB = 10 inches
BC = 15 inches
The length of the third side in a generic triangle can be calculated using the cosine theorem:
[tex]a=\sqrt{b^2+c^2-2bc cos \alpha}[/tex]
where
a, b, c are the three sides
[tex]\alpha[/tex] is the angle opposite to side [tex]a[/tex]
Looking at the formula, we observe that:
- The maximum value for [tex]a[/tex] is obtained for [tex]\alpha=180^{\circ}[/tex], so that [tex]cos \alpha = -1[/tex]. In this case, the length of the missing side (AC, in this case) is
[tex]AC=\sqrt{10^2+15^2-2(10)(15)(-1)}=25 in[/tex]
- The minimum value for [tex]a[/tex] is obtained for [tex]\alpha=0^{\circ}[/tex], for which [tex]cos \alpha =1[/tex], so in this case the length of AC is
[tex]AC=\sqrt{10^2+15^2-2(10)(15)(1)}=5 in[/tex]
So, the length of AC must be between 5 and 25 inches.
