SOLUTION: Dear Sir/Madam; Kindly help me with this problem, I am not familiar with this type of problem. here it is: A triangular lot has two of its angles measuring 25 degrees and

Algebra ->  Trigonometry-basics -> SOLUTION: Dear Sir/Madam; Kindly help me with this problem, I am not familiar with this type of problem. here it is: A triangular lot has two of its angles measuring 25 degrees and       Log On


   



Question 826039: Dear Sir/Madam;
Kindly help me with this problem, I am not familiar with this type of problem. here it is:
A triangular lot has two of its angles measuring 25 degrees and 79 degrees respectively. The longest side has a measure of 26 meters. What are the measures of the other two sides?
Thank you very much for your help!

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Dear Sir/Madam;
Kindly help me with this problem, I am not familiar with this type of problem. here it is:
A triangular lot has two of its angles measuring 25 degrees and 79 degrees respectively. The longest side has a measure of 26 meters. What are the measures of the other two sides?
Thank you very much for your help!

Sketch ΔABC, with angle A, 25o, and angle B, 79o. Now, since angles A and B total 104o, then angle C MUST measure 76o.
Thus, angle B is the largest angle, which means that side AC, or b, which is OPPOSITE angle B is the longest side,
at 26 meters.
The Law of Sines can then be used to determine sides BC (a), and AB (c), the shortest and middle sides
Determining side BC, or a (shortest side)
sin+B%2Fb+=+sin+A%2Fa
sin+79%2F26+=+sin+25%2Fa
a * sin 79 = 26 * sin 25 ------- Cross-multiplying
a = %2826+%2A+sin+25%29%2Fsin+79
a, or side BC, or shortest side = 11.1937 ≈ highlight_green%2811.2%29 m
Determining side AB, or c (middle side)
sin+B%2Fb+=+sin+C%2Fc
sin+79%2F26+=+sin+76%2Fc
c * sin 79 = 26 * sin 76 ------- Cross-multiplying
c = %2826+%2A+sin+76%29%2Fsin+79
c, or side AB, or middle side = 25.699 ≈ highlight_green%2825.7%29 m
You can do the check!!
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