As shown in the illustration, the sides of the right-sided triangle are designated a, b, and c. The angles opposite each of these sides are designated A, B, and C respectively.
Angle A, opposite the hypotenuse a is the right angle, and is therefore always one of the known quantities.

Sides and Angles Known

Formulas for Sides and Angles to be Found

Sides a and b

c=

sin B=b/a

C=90°-B

Sides a and c

b=

sin C=c/a

B =90°-C

Sides b and c

a=

tan B=b/c

C=90°-B

Side a; Angle B

b=a×sin B

c=a×cos B

C=90°-B

Side a; Angle C

b=a×cos C

c=a×sin C

B=90°-C

Side b; Angle B

a=b /sin B

c=b×cot B

C=90°-B

Side b; Angle C

a=b /cos C

c=b×tan C

B=90°-C

Side c; Angle B

a=c /cos B

b=c×tan B

C=90°-B

Side c; Angle C

a=c /sin C

b=c×cot C

B=90°-C

As shown in the illustration, the dimensions of the equal sided and angled octagon are designated F and D. The angles between any two sides is 135° and between corners from center is 45°. A = area.

Dimension Known

Formulas for Area or dimension to be found

F

A=F²×.82842

D=F×1.08268

S=F×.4141

S

A=S²×4.83195

D=S×2.16478

F=S×2.4151

D

A=D²×.70673

S=D×.3825

F=D×.92364