# 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:

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

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