SOLUTION: Given: △АВС, m∠ACB = 90° CD ⊥ AB , m∠ACD = 30°, AC = 8 cm Find: Perimeter of △ABC

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Question 1189247: Given: △АВС, m∠ACB = 90° CD ⊥ AB , m∠ACD = 30°, AC = 8 cm Find: Perimeter of △ABC
Found 2 solutions by greenestamps, MathTherapy:
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Here is a figure. Use the ratio 1:sqrt%283%29:2 for the side lengths of a 30-60-90 right triangle to find the lengths of the sides of triangle ABC.



(1) In triangle ADC, use AC=8 and ACD=30 degrees to determine AD and DC.
(2) In triangle CDB, use CD from (1) and angle BCD=60 degrees to determine AB and BD.

Your final answer for the perimeter of triangle ABC should be 24%2B8sqrt%283%29

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
Given: △АВС, m∠ACB = 90° CD ⊥ AB , m∠ACD = 30°, AC = 8 cm Find: Perimeter of △ABC
AC, the shorter leg of ΔABC is given as 8 cm.

BC, the longer leg of ΔABC = matrix%281%2C2%2C+8sqrt%283%29%2C+%22cm.%22%29

AB, the hypotenuse of △ABC = 2(8) = 16 cm.

Perimeter of △ABC =