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Angelina_Jolie [31]
3 years ago
8

matt is standing on top of a cliff 305 feet above a lake. The measurement of the angle of depression to a boat on a lake is 42 d

egrees. how far is the boat from matt

Mathematics
1 answer:
Lyrx [107]3 years ago
3 0

Answer:

So, the distance from boat to matt is 455.81535feet

Step-by-step explanation:

We are given height of a cliff is 305 feet

and the measurement of the angle of depression to a boat on a lake is 42 degrees

so, we can draw diagram

Let's assume

distance from boat to matt is x

We can use trig

sin(42)=\frac{305}{x}

now, we can solve for x

x=\frac{305}{sin(42)}

x=455.81535feet

So, the distance from boat to matt is 455.81535feet

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Answer:

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Step-by-step explanation:

Given the following :

Speed of child due east = 3mph

Speed of ship due North = 16mph

Relative speed of th child is obtained by using Pythagoras rule to find the hypotenus

Relative Speed = Sqrt(3² + 16²)

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From trigonometry ;

Tanθ = opposite / Adjacent

Tanθ = (16 / 3)

Tanθ = 5.333

θ = tan^-1(5.333)

θ = 79.379°

θ = 79.38°

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