Two buildings are 35 feet apart. The angle of elevation from the top of the smaller building to the top of the taller building i
s 42˚. The smaller building is 32 feet high. Find the height of the taller building.
1 answer:
Answer:
Height of the taller building is 63.5ft
Step-by-step explanation:
Kindly find attached rough sketch of the problem for your reference.
Let the small building be A and the taller building be B
From the sketch the two buildings form a right angle triangle
We can solve for x which is the height of the taller building relative to the small building using
SOH CAH TOA
Applying TOA we have
Tan θ= opposite/adjacent
Tan 42°= x/35
x= Tan 42*35
x= 0.9*35
x= 31.5ft
Hence the height of the taller building is = x+height of small building = 31.5+32= 63.5ft
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Answer:
The correct option is;
No, The greater rate of change of Plant A will result in it being 0.9 inches taller in 6 weeks
Step-by-step explanation:
The parameters given are;
Plant A:
Weeks, Height
0, 3
1, 4.8
2, 6.6
3, 8.4
The rate of change of height, H per week, t, for plant A per week is therefore;
Therefore we have;
H = 1.8 × t + 3
At week 6,
H = 3 + 6×1.8 = 13.8 inches
Plant B
Weeks, Height
2, 7.3
3, 8.7
4, 10.1
The rate of change of height, H per week, t, for plant B per week is given as follows;
Therefore we have;
When t = 2, H = 7.3 hence, 7.3 = 2 × 1.4 + H₀
Where:
H₀ = H at t = 0
H₀ = 7.3 - 2 × 1.4 = 4.5
At week 6 we have;
H = 4.5 + 6×1.4 = 12.9 inches
Which indicates that Plant A will be 0.9 inches taller than Plant B at week 6.
The correct option is therefore;
No, The greater rate of change of Plant A will result in it being 0.9 inches taller in 6 weeks.