Respuesta :
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;
[tex] \frac{15}{sin( 46 ^ \circ)} = \frac{Gwen \: to \: Hadley}{sin( 61 ^ \circ)} [/tex]
Which gives;
[tex] Gwen \: to \: Hadley= \frac{15 \times sin( 61 ^ \circ) }{sin( 46 ^ \circ)} \approx 18.24[/tex]
- Gwen to Hadley ≈ 18.24 meters
Similarly, we have;
[tex] \frac{15}{sin( 46 ^ \circ} = \frac{Gwen \: to \: James}{sin( 73 ^ \circ)} [/tex]
Therefore;
[tex] Gwen \: to \: James = \frac{15 \times sin( 73 ^ \circ) }{sin(46 ^ \circ)} \approx 19.94 [/tex]
- Gwen to James ≈ 19.94 meters
Learn more about the rule of sines here:
https://brainly.com/question/4372174
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