SOLUTION: In △ABC, AC = BC, AB = 6, m∠BAC = 71º. Find the length of the altitude AH.

Algebra ->  Trigonometry-basics -> SOLUTION: In △ABC, AC = BC, AB = 6, m∠BAC = 71º. Find the length of the altitude AH.       Log On


   

Question 1147423: In △ABC, AC = BC, AB = 6, m∠BAC = 71º. Find the length of the altitude
AH.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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Lower triangle with AB on the bottom

Triangle AHB
AB=6
Angle at A is 19 degree
Angle at B is 71 degree
point H at angle of 90 degree
AH wanted

AH%2F6=sin%2871%29

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

Given triangle ABC is isosceles; therefore, the altitude AH is the median, at same time.


It means that  AH = BH = 6/2 = 3 units of length.


Then  tan(A) = abs%28AH%29%2F3,   or


      tan(71°) = abs%28AH%29%2F3,


which implies  | AH | = 3*tan(71°).      ANSWER

Solved.

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Be aware :   the solution by  @josgarithmetic giving the answer  AH%2Fsin%2871%29=6%2Fsin%2890%29  is   I N C O R R E C T (!)

I came to bring the correct solution.