Answer :
Answer:
The boat is 8.4m out of the sea
Step-by-step explanation:
Kindly find attached rough sketch of the problem.
From the sketch we can see that the observer from the cliff and the horizontal distance forms a right angle triangle
Let the horizontal distance be x
Let the angle of elevation from the boat be y
Applying sum of angles in a triangle
90+6+y= 180
96+y=180
y=180-96
y= 84°
Applying SOH CAH TOA
Using TOA
Tanθ= opposite /adjacent
Tan 84= 80/x
x= 80/tan 84
x= 80/9.51
x= 8.4m
The distance of the boat to the cliff is 762m.
The situation forms a right angle triangle.
Right angle triangle
Right angle triangle are triangle that has one of its angle as 90 degrees. The sides can be found using trigonometric ratio.
Therefore,
The height of the vertical cliff is the opposite side of the triangle formed.
The distance from the boat to the cliff is the adjacent side.
Therefore,
tan 6 = opposite / adjacent
tan 6 = 80 / a
cross multiply
a = 80 / tan 6
a = 80 / 0.10510423526
a = 761.904761905
a = 762 m
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