SOLUTION: In ∆ABC, m∠C = 90º, m∠A = 50º, AB = 35. Find the length of the altitude CH.

Algebra ->  Trigonometry-basics -> SOLUTION: In ∆ABC, m∠C = 90º, m∠A = 50º, AB = 35. Find the length of the altitude CH.       Log On


   

Question 1147591: In ∆ABC, m∠C = 90º, m∠A = 50º, AB = 35. Find the length of the altitude CH.

Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Draw and label the figure.
If x is distance HB, then 35-x is distance HA.
Interior angle at point B is 40 degrees.

system%28CH%2F%2835-x%29=tan%2850%29%2CCH%2Fx=tan%2840%29%29;
Goal is solve for CH.
.
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Answer by ikleyn(52908) About Me  (Show Source):
You can put this solution on YOUR website!
.

In triangle ABC, you are given the hypotenuse AB = 35 units and two adjacent angles A of 50°  and B of 40°.


Then one leg is  35*sin(50°)  and the other leg is 35*sin(40°).


The area of the triangle is then  A = %281%2F2%29%2A35%5E2%2Asin%2840%5Eo%29%2Asin%2850%5Eo%29.


From the other side, the area of the triangle is  A = %281%2F2%29%2A35%2Aabs%28CH%29.


From the equation


    %281%2F2%29%2A35%5E2%2Asin%2840%5Eo%29%2Asin%2850%5Eo%29 = %281%2F2%29%2A35%2Aabs%28CH%29


you have  | CH | = 35*sin(40°)*sin(50°).


Use your calculator if you want to get the numerical value.

Solved.

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Ignore the post by @josgarithmetic, since it is infinitely far from to be a true solution.