Question

In math class, James, Hadley, and Gwen were challenged to go stand on the field in a random location and find the distance between themselves using only one length. They were also each given a protractor to find the angle between each other. Using this diagram, solve for the missing side lengths of the triangle. Round to the nearest hundredth. A triangle where James, Hadley, and Gwen are labelled on the vertices. The angle of James is 61 degrees, Hadley is 73 degrees, and Gwen is 46 degrees. The one length that is labelled is between James and Hadley and measures at 15 meters. Gwen to Hadley is what? Gwen to James is what?

Answer 1

The interior angles of the triangle of 61°, 73°, and 46°, and the distance from James to Hadley of 15 meters gives;

• Gwen to Hadley ≈ 18.24 meters

• Gwen to James ≈ 19.94 meters

How can the distances between the students be found?

The given angles are;

At James's location; 61°

At Hadley's location; 73°

At Gwen's location; 46°

The distance between James and Hadley = 15 meters

The angle facing the distance between James and Hadley is the angle at Gwen, 46°

The angle facing the distance between Gwen and James is the angle at Hadley, 73°

The angle facing the distance between Gwen and Hadley is the angle at James, 61°

The angle that faces the 15 meter length is the angle at Gwen, which is 46°

By the rule of sines, the distance from Gwen to Hadley is therefore;

$\frac{15}{sin( 46 ^ \circ)} = \frac{Gwen \: to \: Hadley}{sin( 61 ^ \circ)}$

Which gives;

$Gwen \: to \: Hadley= \frac{15 \times sin( 61 ^ \circ) }{sin( 46 ^ \circ)} \approx 18.24$

• Gwen to Hadley ≈ 18.24 meters

Similarly, we have;

$\frac{15}{sin( 46 ^ \circ} = \frac{Gwen \: to \: James}{sin( 73 ^ \circ)}$

Therefore;

$Gwen \: to \: James = \frac{15 \times sin( 73 ^ \circ) }{sin(46 ^ \circ)} \approx 19.94$

• Gwen to James ≈ 19.94 meters

Learn more about the rule of sines here:

https://brainly.com/question/4372174

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