Trig/geometry help (triangles/finding sides)

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To find side 'R' in the triangle, given L = 6.10 meters, theta = 36.9 degrees, and phi = 53.1 degrees, the Law of Sines can be applied. By drawing a vertical line through the triangle and recognizing that phi is the angle between this vertical line and the triangle's side, the relationship can be established. The equation L/sin(phi + theta) = R/cos(phi) is derived to solve for R. The discussion emphasizes the need to visualize the triangle and apply trigonometric principles correctly. Understanding the relationships between the angles and sides is crucial for finding the unknown side.
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Homework Statement


h83RV.png

Find side 'R'. L = 6.10 meters, theta = 36.9 degrees, and phi = 53.1 degrees.

Homework Equations


Pythagorean Theorem
Similar triangles
Law of Sines
Law of Cosines

The Attempt at a Solution


I don't see any way I can attempt this, I'm very rusty with my trig. We have a known side and a right angle, but I don't see how I can make any other angles (since we only have one side I'm assuming I need to get an angle somewhere
 
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PhizKid said:

Homework Statement


h83RV.png

Find side 'R'. L = 6.10 meters, theta = 36.9 degrees, and phi = 53.1 degrees.

Homework Equations


Pythagorean Theorem
Similar triangles
Law of Sines
Law of Cosines

The Attempt at a Solution


I don't see any way I can attempt this, I'm very rusty with my trig. We have a known side and a right angle, but I don't see how I can make any other angles (since we only have one side I'm assuming I need to get an angle somewhere

Draw a vertical line through the right side of the length L (the point on the triangle). The length L will be perpendicular to this line, yes? And now take notice that \phi would be the angle between the vertical and the side of the triangle because of the parallel lines rule (the wall is parallel to the vertical line we constructed).
 
law of sines gives

L/sin(phi+theta)=R/cos(phi)
 

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