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1 answer:
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Answer with Step-by-step explanation:
We are given that a sample space
S={a,b,c,d,e}
P(a)=0.1
P(b)=0.1
P(c)=0.2
P(d)=0.4
P(e)=0.2
a.A={a,b,c}
P(A)=P(a)+P(b)+P(c)
P(A)=0.1+0.1+0.2=0.4
b.B={c,d,e}
P(B)=P(c)+P(d)+P(e)=0.2+0.4+0.2=0.8
c.A'=Sample space-A={a,b,c,d,e}-{a,b,c}={d,e}
P(A')=P(d)+P(e)=0.4+0.2=0.6
d.={a,b,c,d,e}
=P(a)+P(b)+P(c)+P(d)+P(e)=0.1+0.1+0.2+0.4+0.2=1
e.={c}
Answer:
The height of the next door building is 41.7 feet
Step-by-step explanation:
* Lets study the situation in the problem
- The man standing on the roof of a building 64.0 feet high
- The angle of depression to roof of the next door building is 34.7°
- The angle of depression to the bottom of the next door building
is 63.3°
- We need to find the height of the next door building
* Lets consider the height of the man building and the horizontal
distance between the two building formed a right triangle and the
angle of depression is opposite to the side which represented the
height of the building
- Let the horizontal distance between the two buildings called x
# In the triangle
∵ The length of the side opposite to the angle of depression (63.3°)
is 64.0
∵ The length of the horizontal distance is x which is adjacent to the
angle of depression (63.3°)
- Use the trigonometry function tanФ = opposite/adjacent
∴ tan 63.3° = 64.0/x ⇒ use cross multiplication
∴ x (tan 63.3°) = 64 ⇒ divide both sides by (tan 63.3°)
∴ x = 64.0/(tan 63.3°)
∴ x = 32.1886 feet
- Lets use this horizontal distance to find the vertical distance between
the roofs of the two buildings
* Lets consider the height of the vertical distance between the roofs
of the two buildings and the horizontal distance between the two
building formed a right triangle and the
angle of depression is opposite to the side which represented the
vertical distance between the roofs of the two buildings
- Let the vertical distance between the roofs of the two buildings
called y
# In the triangle
∵ The vertical distance between the roofs of the two buildings is y
and opposite to the angle of depression (34.7°)
∵ The horizontal distance x is adjacent to the angle of
depression (34.7°)
∴ tan (34.7°) = y/x
∵ x = 32.1886
∴ tan 34.7° = y/32.1886 ⇒ use the cross multiplication
∴ y = 32.1886 (tan 34.7°)
∴ y = 22.2884 ≅ 22.3 feet
∴ The vertical distance between the roofs of the two
buildings is 22.3 feet
- The height of the next door building is the difference between the
height of the man building and the vertical distance between the
roofs of the two buildings
∴ The height of the next door building = 64.0 - 22.3 = 41.7 feet
