The top of the cliff is 142 m above sea level. Currently the boat is 100 metres from the buoy and the angle of depression from the top of the cliff to the boat is 64º. Find the distance from the top of the cliff to the buoy. diagram not to scale Top of cliff 142 boat buoy Base of cliff (sea level) 100 m. The distance from the top of the cliff to the buoy is type your answer...

221.0 m

Step-by-step explanation:

First, find x using trigonometric ratio formula:

Reference angle = angle of depression = angle of elevation = 64°

Opposite side length = 142 m

Adjacent side length = x

Thus:

tan(64) = 142/x

x*tan(64) = 142

x = 142/tan(64)

x = 69.3 (nearest tenth)

Next, find distance from top of the hill to the buoy using Pythagorean Theorem.

Let the distance be y.

We would have:

y² = 142² + (69.3 + 100)²

y² = 20,164 + 28,662.49

y² = 48,826.49

y = √48,826.49

y = 221.0 m (nearest tenth)

the correct answer is 5 6 and 7

exa:

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3+11

14

step-by-step explanation:

from this example, we can see that subtracting with integers is the same as adding the opposite. we can solve using a number line or by using the saying "keep, change, change" to us solve. it is important to remember that we can subtract a negative and end up with a larger number than we started with.