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Round to the nearest tenth.

At a point on the ground 50 feet from a tree, the angle of elevation to the top of the tree is 48 degrees. Find the height of the tree.

User Maelga
by
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1 Answer

5 votes

Answer:

Explanation:

We can use trigonometry to solve this problem. Let's draw a diagram to visualize the situation:

*

/|

/ |

/ |

/ | h

/ |

/ |

/48° |

/_______|

50 ft

We can use trigonometry to solve this problem. Let's draw a diagram to visualize the situation:

perl

Copy code

*

/|

/ |

/ |

/ | h

/ |

/ |

/48° |

/_______|

50 ft

In this diagram, the height of the tree is represented by "h", and the angle of elevation to the top of the tree is 48 degrees. We also know that the distance from the tree to the point on the ground is 50 feet.

We can use the tangent function to relate the angle of elevation to the height of the tree:

tan(48°) = h / 50

Simplifying this equation for h, we get:

h = 50 * tan(48°)

Using a calculator, we can evaluate tan(48°) to be approximately 1.1918. Substituting this value in the equation, we get:

h = 50 * 1.1918 = 59.59

Therefore, the height of the tree is approximately 59.59 feet.

User Med Tumy
by
7.7k points