Answer:
881.5 meters.
Step-by-step explanation:
The horizontal plane at the level of wai-kin's eyes divide the height of the cliff into two parts. Let the upper part be represented by x and the lower part be represented by y.
The height of the cliff = x + y
Applying the appropriate trigonometry functions.
To determine the value of x;
Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
Tan [tex]36^{o}[/tex] = [tex]\frac{x}{490}[/tex]
⇒ x = 490 x Tan [tex]36^{o}[/tex]
= 490 x 0.7265
= 355.985
x = 356 meters
To determine the value of y;
Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
Tan [tex]47^{o}[/tex] = [tex]\frac{y}{490}[/tex]
⇒ y = 490 x Tan [tex]47^{o}[/tex]
= 490 x 1.0724
= 525.476
y = 525.5 meters
Therefore,
The height of the cliff = x + y
= 355.985 + 525.476
= 881.461
The height of the cliff is 881.5 meters.
