Question

A pole is braced by two wires that extend from the top of the pole to the ground. The lengths of the wires are 16 feet and 18 feet and the measure of the angle between the wires is $110^{\circ} .$ Find, to the nearest foot, the distance between the points at which the wires are fastened to the ground.

Name: Problem 23, Chapter 14: Algebra 2 and Trigonometry
Uploaded: 2020-05-25T17:04:52-08:00
Duration: 1 min 24 s
Channel: Katelyn Chen
Description: A pole is braced by two wires that extend from the top of the pole to the ground. The lengths of the wires are 16 feet and 18 feet and the measure of the angle between the wires is 110^∘ . Find, to the nearest foot, the distance between the points at which the wires are fastened to the ground.

   A pole is braced by two wires that extend from the top of the pole to the ground. The lengths of the wires are 16 feet and 18 feet and the measure of the angle between the wires is $110^{\circ} .$ Find, to the nearest foot, the distance between the points at which the wires are fastened to the ground.

Algebra 2 and Trigonometry

Ann Xavier Gantert 1st Edition

Chapter 14, Problem 23

Instant Answer

Solved by Expert Katelyn Chen

05/25/2020

Step 1

The lengths of the wires are 16 feet and 18 feet, and the angle between the wires is $110^{\circ}$. We are asked to find the distance between the points at which the wires are fastened to the ground. This distance forms the third side of the triangle, which we Show more…

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A pole is braced by two wires that extend from the top of the pole to the ground. The lengths of the wires are 16 feet and 18 feet and the measure of the angle between the wires is $110^{\circ} .$ Find, to the nearest foot, the distance between the points at which the wires are fastened to the ground.

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Key Concepts

Law of Cosines

The Law of Cosines provides a relationship between the lengths of sides of any triangle and the cosine of one of its angles. It is especially useful in solving triangles when two sides and the included angle are known, allowing for the calculation of the third side.

Triangle Geometry

Triangle geometry focuses on the properties and relationships inherent to triangles, including the connections between side lengths and angles. This understanding is fundamental in formulating geometric solutions to problems involving distances and angles.

Trigonometry

Trigonometry is the branch of mathematics that studies the relationships among the angles and lengths of triangles. It encompasses functions like cosine, which play a vital role in applying formulas such as the Law of Cosines to real-world problems.

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