Finding side R given L = 6.10 m, theta = 36.9°, phi = 53.1°

[PhizKid]

Homework Statement

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

 

[Mentallic]

Homework Statement

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).

 

[lurflurf]

law of sines gives

L/sin(phi+theta)=R/cos(phi)