Given the right triangle ABC with right angle C mBAD alpha

Given the right triangle ABC with right angle C, m(BAD) = alpha and m(ADC) = beta. If sin a = 1/5 and beta = 1/4; find tan (ABC) = ? (You do not need simplify your answer.)

Solution

Sin() = 1/5 ======> = 11.5

Sin() = AC/AD = ¼ ======> = 14.5

In Triangle ADC, Angle BAC = 180 – (90 + ) - = 90 – -

Then Angle ABC = 180 - (90 + 90 - – ) = ( + ) = 11.5 + 14.5 = 26

Then Tan(ABC) = tan26 = 0.488