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An object is inclined at an angle of elevation of 56 degrees
from the base of a hill whose distance is K m. What is the observing
distance of the object if the heigth of the hill must be 8m. Give the
answers to the nearest whole number or two decimal places. See
figure 1 for details.
The heigth of the hill is 8m
The angle of inclination is 56 d.
The diagram of the question is shown as figure 1.
SinQ = Opp / Hyp
Sin(56) = 8 / L
cross multiply
L x Sin(56) = 8
L = 8 / Sin(56)
L = 8 / (0.82904)
L = 9.6497
L = 9.65 (Approximate)
L = 9.65 m
The observing distance of the object which is the hypotenus
is equal to 9.65m.
CosQ = Adj / Hyp
TanQ = Opp / Adj
Tan(56) = 8 / K
cross multiply
K x Tan(56) = 8
K = 8 / Tan(56)
K = 8 / (1.4826)
K = 5.396
K = 5.4 (Approximate)
K = 5.4m.
The distance of the object from the base/bottom of the hill
is equal to 5.4m. The observing distance which is the hypothenus
of the shape(triangle) is 9.65m approximately.
