Answer:
The length of the island is 699 feet.
Step-by-step explanation:
Let the distance from the foot of the cliff to the near side be represented by x, and the distance from the foot of the cliff to the far side be represented by y.
Applying the trigonometric function to calculate the value of x;
Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
Tan [tex]16^{o}[/tex] = [tex]\frac{320}{x}[/tex]
0.2867 = [tex]\frac{320}{x}[/tex]
x = [tex]\frac{320}{0.2867}[/tex]
= 1116.1493
x = 1116.15 feet
The distance from the foot of the cliff to the near side of the island is 1116.15 feet.
To determine the value of y;
Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
Tan [tex]10^{o}[/tex] = [tex]\frac{320}{y}[/tex]
0.1763 = [tex]\frac{320}{y}[/tex]
y = [tex]\frac{320}{0.1763}[/tex]
= 1815.0879
y = 1815.09 feet
The distance from the foot of the cliff to the far side of the island is 1815.09 feet.
The length of the island = y - x
= 1815.09 - 1116.15
= 698.94
The length of the island is 699 feet.
