Solve the triangle: side a=3, side b=2, side c= 2.

Find area of triangle: a=2,b=1,theta=100(degrees) <--the angle between them

A triangle has interior angles of measure (2x+9)°, (3x-14)°, and (5x+20)°. Find the smallest interior angle of this triangle.

(2x+9)°+(3x-14)°+(5x+20)°=180
10x+15=180
10x=165
x=16.5
the least angle is 3(16.5)-14=35.5 degrees 

In OPQ, o = 870 inches, P = 80 degrees, and Q = 9 degrees. Find the length of p to the nearest 10th of an inch.

We'll denote the measure of angle X as

In any triangle the sum of the angles is 180 degrees, so

so we know

Now using the Law of Sines we write:



which leads to

In ∆ABC, if the length of sides a, b, and c are 3.5 centimeters, 5.5 centimeters, and 6 centimeters respectively, what is m C to two decimal places?

law of cosines:

C=arccos(13/77)=80.28 degrees

solve triangle XYZ where angle X=40, x=12 and y=6

Law of Sines: sinY=(6/12)sin40
sinY=0.3214
Y=arcsine(0.3214)
Y=18.747

Since all angles must add to 180 degrees:
Z=180-40-18.747=121.25
now we find z...
z=12(sin121.25/sin40)=15.96 

A triangle has 45, 105 and 30 degree angles the smallest side is 8. What is the perimeter?

We can use the Law of Sines: 

 
 
 
 


 

rounded...P=34.77

Find the remaining angles and sides of each triangle if it (they) exists. If no triangle exists, say “no triangle” A=10(degrees), B=40 (degrees), side c=2

A=10(degrees), B=40 (degrees), side c=2




Solution:

A=10deg, B=40deg, c=2 

First let's find the missing angle: 

 

We can solve this triangle by using the Law of Sines. 



 

which is approximately 0.453 
Similarly...

 

which is approximately 1.678

Solve the triangle: B=86 deg, C=17 deg, 42 min, and b=23

Solve the triangle

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