Answer:
The raft is 16.57 feet far away from the ship.
Step-by-step explanation:
To find the distance of the raft from the ship if the angle of depression to a raft from a watch site on a ship is 10° and the site is 94 feet above sea level, we will follow the step below:
We can solve the problem using the trig. ratio
That is;
SOH CAH TOA
sin Ф = opposite / hypotenuse
cosФ= adjacent/hypotenuse
tanФ=opposite/adjacent
From the figure below;
angle Ф = 10°, we have adjacent= 94 feet and opposite =x where x is the distance of the raft from the ship.
so the best trig. ratio to use is tan
tanФ=opposite/adjacent
We can now proceed to insert the values into the formula
tan 10 = [tex]\frac{X}{94}[/tex]
multiply both-side of the equation by 94
94 × tan 10 = [tex]\frac{X}{94}[/tex] × 94
At the right-hand side of the equation, 94 will cancel-out 94 leaving us with just x
94 tan 10 = x
16.57 ≈ x
x≈16.57 feet
Therefore, the raft is 16.57 feet far away from the ship.
