● Solve a right triangle. | |||||||||||||||||||||||||
● Solve a 45-45-90 triangle. | ● Solve a 30-60-90 triangle. | Often these may be computed mentally. | |||||||||||||||||||||||
Input leg a. | |||||||||||||||||||||||||
A is | 30 | a is | 1.000 | ||||||||||||||||||||||
B is | 60 | b is | 1.732 | ||||||||||||||||||||||
C is | 90 | c is | 2.000 | ||||||||||||||||||||||
a=c/2, a=b/√(3) | |||||||||||||||||||||||||
b=a√(3), b=c√(3)/2 | |||||||||||||||||||||||||
c=2a, c=2b/√(3) | |||||||||||||||||||||||||
Often these may be computed mentally. | Often these may be computed mentally. | ||||||||||||||||||||||||
Input leg a or side c. | Input leg b. | Input side c. | |||||||||||||||||||||||
A is | 45 | a is | 5.000 | A is | 30 | a is | 1.000 | A is | 30 | a is | 1.000 | ||||||||||||||
B is | 45 | b is | 5.000 | B is | 60 | b is | 1.732 | B is | 60 | b is | 1.732 | ||||||||||||||
C is | 90 | c is | 7.071 | A is | 90 | c is | 2.000 | C is | 90 | c is | 2.000 | ||||||||||||||
a=b, a=c/√2, c=a√2 | a=c/2, a=b/√(3) | a=c/2, a=b/√(3) | |||||||||||||||||||||||
A is | 90 | a is | 8.485 | b=a√(3), b=c√(3)/2 | b=a√(3), b=c√(3)/2 | ||||||||||||||||||||
B is | 45 | b is | 8.485 | c=2a, c=2b/√(3) | c=2a, c=2b/√(3) | ||||||||||||||||||||
C is | 90 | c is | 12.000 | ||||||||||||||||||||||
● Use Pythagorean Theorem and arithmetic and basic trig. | A is | a is | A is | a is | |||||||||||||||||||||
B is | b is | B is | b is | ||||||||||||||||||||||
C is | c is | C is | c is | ||||||||||||||||||||||
A is | a is | A is | a is | ||||||||||||||||||||||
B is | b is | B is | b is | ||||||||||||||||||||||
C is | c is | C is | c is | ||||||||||||||||||||||
A is | a is | A is | a is | ||||||||||||||||||||||
B is | b is | B is | b is | ||||||||||||||||||||||
Input leg a and leg b. | Input hypotenuse c and leg a. | Input angle A and side a. | C is | c is | C is | c is | |||||||||||||||||||
A is | 22.619864948 | a is | 5.000 | A is | 45.0086542764 | a is | 1.000 | A is | 60 | a is | 1.732 | ||||||||||||||
B is | 67.380135052 | b is | 12.000 | B is | 44.9913457236 | b is | 1.000 | B is | 30 | b is | 1.000 | A is | a is | A is | a is | ||||||||||
C is | 90 | c is | 13.000 | C is | 90 | c is | 1.414 | C is | 90 | c is | 2.000 | B is | b is | B is | b is | ||||||||||
A is =ArcSIN(a/c)*180/PI() | A is =ArcSIN(a/c) | B is =90-A | C is | c is | C is | c is | |||||||||||||||||||
B is =90-A | B is =ArcSIN(b/c) | C is 90. | |||||||||||||||||||||||
C is =90 | C is 90. | b is =a/TAN(A*PI()/180) | |||||||||||||||||||||||
c is =SQRT(a^2+b^2) | b is =SQRT(c^2-a^2) | c is =SQRT(a^2+b^2) | |||||||||||||||||||||||
● Solve any triangle. | |||||||||||||||||||||||||
● Use the Sine Law, | A is | 10 | a is | 44.000 | |||||||||||||||||||||
B is | 12 | b is | 56.469 | ||||||||||||||||||||||
C is | 14.156 | c is | 56.469 | ||||||||||||||||||||||
A is | 10 | a is | 79.531 | ||||||||||||||||||||||
B is | 12 | b is | 123.531 | ||||||||||||||||||||||
C is | 3.108 | c is | 12.469 | ||||||||||||||||||||||
A is | a is | ||||||||||||||||||||||||
B is | b is | ||||||||||||||||||||||||
C is | c is | ||||||||||||||||||||||||
● If given a side and opposite angle. | |||||||||||||||||||||||||
Input angles A , B, side a. | Input angle A , side a, side b. | A is | a is | ||||||||||||||||||||||
a is | 1.000 | A is | 30.000 | a is | 9.000 | A is | 44.000 | a | bsin(A) | a | b | B is | b is | ||||||||||||
b is | 1.732 | B is | 60.000 | b is | 11.000 | B is | 58.106 | no solution | 9.000 | < | 7.641242075 | if #NUM! there is no solution. | C is | c is | |||||||||||
c is | 2.000 | C is | 90.000 | c is | 12.668 | C is | 77.894 | 1 solution | 9.000 | = | 7.641242075 | ||||||||||||||
C is =180-A-B | b2 is | 11.000 | B2 is | 121.894 | 2 solutions | 7.641242075 | < | 9.000 | < | 11.000 | |||||||||||||||
b is a*sin(B)/sin(a) | c2 is | 3.158 | C2 is | 14.106 | 1 solution | 9.000 | > | 11.000 | |||||||||||||||||
c is =arcsin(c*SIN(A)/a) | B is =ArcSIN(G37*SIN(I36*PI()/180)/G36)*180/PI() | ||||||||||||||||||||||||
C is 180-A-B | |||||||||||||||||||||||||
c is =a*SIN(C*PI()/180)/SIN(A*PI()/180) | |||||||||||||||||||||||||
b2=b1 | |||||||||||||||||||||||||
B2=180-B | |||||||||||||||||||||||||
c2=a*SIN(C2*PI()/180)/SIN(A*PI()/180) | |||||||||||||||||||||||||
● Use the Law of Cosines, | A is | 46.145 | a is | 4.000 | |||||||||||||||||||||
● If not given a side and opposite angle. | B is | 115.66 | b is | 5.000 | |||||||||||||||||||||
Input sides a, b, c. | Input angle A , sides b,c. | C is | 18.194 | c is | 1.730 | ||||||||||||||||||||
A is | 36.8698976458 | a is | 3 | A is | 36.87 | a is | 3.0000071457 | ||||||||||||||||||
B is | 53.1301023542 | b is | 4.00 | B is | 53.130102354 | b is | 4.00 | A is | a is | ||||||||||||||||
C is | 90 | c is | 5.00 | C is | 89.999897646 | c is | 5.000 | B is | b is | ||||||||||||||||
A is =arccos((b^2+c^2-a^2)/2*b*c))*(180/pi()) | a is =sqrt(b^2+c^2-2bccos(A*pi()/180)) | C is | c is | ||||||||||||||||||||||
B is =arccos((a^2+c^2-b^2)/2*a*c))*(180/pi()) | B is =arccos((a^2+c^2-b^2)/2*a*c))*(180/pi()) | ||||||||||||||||||||||||
C is =arccos((a^2+b^2-c^2)/2*a*b))*(180/pi()) | C is =arccos((a^2+b^2-c^2)/2*a*b))*(180/pi()) | A is | a is | ||||||||||||||||||||||
B is | b is | ||||||||||||||||||||||||
C is | c is | ||||||||||||||||||||||||
A is | a is | ||||||||||||||||||||||||
B is | b is | ||||||||||||||||||||||||
C is | c is | ||||||||||||||||||||||||
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