Answer:
8 miles
Step-by-step explanation:
Given
<em>Represent the police station with P, Library with L; Fire station with F</em>
<em>The first statement can be represented as:</em>
<em></em>
<em>The second can be represented as:</em>

Required
Determine the distance between the police station and the fire station (P - F)
--- (1)
--- (2)
Substitute 5 for L - P in (1)

Add 3 to both sides




Theorem of cosine:
a²=b²+c²-2bc(cos α) ⇒cos α=-(a²-b²-c²) / 2bc
In this case:
a=15 cm
b=10 cm
c=5 cm
cos α=-(15²-10²-5²) / 2*10*5
cos α=-100 / 100
cos α=-1
A=arc cos -1=180º This is impossible, because:
A+B+C=180º; then B=C=0º This is impossible for make a triangle (B>0 and C>0 if we want to make a triangle).
Therefore: it is not possible can make a triangle with side lengths of 5 cm, 10 cm and 15 cm.
Answer:
15 cm
Step-by-step explanation:
Given:
The two cylinders shown in the figure are similar to each other.
Therefore, when two figures are similar their measures are in proportion.
So, radius and height of both the cylinders are in proportion.
Radius of both the cylinders are 2 cm and 5 cm respectively. Height of the smaller cylinder is 5 cm. Now,

Doing cross multiply, we get:

Dividing both sides by 2, we get:

Therefore, the height of the larger cylinder must be 15 cm in order to make both the cylinders similar to each other.