Inner angles

The inner angles of the triangle are 30°, 45° and 105° and its longest side is 10 cm. Calculate the length of the shortest side, write the result in cm up to two decimal places.

Result

a =  5.18 cm

Solution:

A=30 B=45 C=105 c=10 cm a/c=sin(A)/sin(C)=sin(30)/sin(105)1.018 a=c sin(Arad=A π180 rad=5.17638090205 rad)/sin(Crad=C π180 rad=5.17638090205 rad)=5.18  cm A = 30 \ \\ B = 45 \ \\ C = 105 \ \\ c = 10 \ cm \ \\ a/c = \sin(A)/\sin(C) = \sin(30)/\sin(105) \doteq 1.018 \ \\ a = c \cdot \ \sin( A \rightarrow rad = A \cdot \ \frac{ \pi }{ 180 } \ rad = 5.17638090205 \ rad)/\sin( C \rightarrow rad = C \cdot \ \frac{ \pi }{ 180 } \ rad = 5.17638090205 \ rad) = 5.18 \ \text { cm }

Try calculation via our triangle calculator.








Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Following knowledge from mathematics are needed to solve this word math problem:

Cosine rule uses trigonometric SAS triangle calculator. See also our trigonometric triangle calculator.