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Rom4ik [11]
2 years ago
11

A flag pole has a rope that attaches to the ground from the top of the flagpole the rope create a 30° angle with the ground and

is attached 10 m from the bottom of the pool how long is the rope in how tall is the flagpole
Mathematics
1 answer:
OLEGan [10]2 years ago
3 0

Answer:

5.77\ \text{m}

11.54\ \text{m}

Step-by-step explanation:

p = Height of pole

h = Length of role

b = Distance between the bottom of the rope and bottom of the pole = 10 m

\theta = Angle between the rope and the ground = 30^{\circ}

\tan\theta=\dfrac{p}{b}\\\Rightarrow p=b\tan\theta\\\Rightarrow p=10\tan30^{\circ}\\\Rightarrow p=5.77\ \text{m}

The length of the rope is 5.77\ \text{m}

\cos\theta=\dfrac{b}{h}\\\Rightarrow h=\dfrac{b}{\cos\theta}\\\Rightarrow h=\dfrac{10}{\cos30^{\circ}}\\\Rightarrow h=11.54\ \text{m}

The length of the pole is 11.54\ \text{m}

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