Answer to Question #90785 in Trigonometry for Unknown287159

Question #90785
Solve triangle ABC given that:A=60° ,AB=12,2cm and BC=14,5.
1
Expert's answer
2019-06-13T08:35:48-0400



We can use The Law of Sines first to find angle C:


"\\frac{AB}{\\sin{C}}=\\frac{BC}{\\sin{A}},"




"\\frac{12.2}{\\sin{C}}=\\frac{14.5 \\cdot 2}{\\sqrt{3}},""C=\\arcsin{\\frac{61\\sqrt{3}}{145}}."



The other angle C might be

"180 \\degree - \\arcsin{\\frac{61\\sqrt{3}}{145}} \\approx 133.23 \\degree,"

but this is impossible, since the sum of the angles A and C is more than 180°.


Use "the three angles add to 180°" to find angle B:


"B = 180\\degree - A - C = 120\\degree - C."



Now we can use The Law of Sines again to find AC:


"\\frac{AC}{\\sin{B}}=\\frac{BC}{\\sin{A}},"


"\\sin{B} = \\sin{(120\\degree - C)} = \\\\ \\sin{120\\degree}\\cos{C}-\\cos{120\\degree}\\sin{C} = \\\\ \\frac{\\sqrt{3}}{2} \\sqrt{1-\\left(\\frac{61\\sqrt{3}}{145}\\right)^2} - \\left(-\\frac{1}{2}\\right) \\cdot \\frac{61\\sqrt{3}}{145} = \\frac{\\sqrt{3}}{290}\\left(\\sqrt{9862}+61\\right),"


"AC = \\frac{14.5 \\cdot 2}{\\sqrt{3}} \\sin{B} = \\frac{1}{10} \\left(\\sqrt{9862}+61\\right)."

Answer:

"C=\\arcsin{\\frac{61\\sqrt{3}}{145}} \\approx 46.77 \\degree,""B = 120\\degree - C \\approx 73.23 \\degree,""AC = \\frac{1}{10} \\left(\\sqrt{9862}+61\\right) \\approx 16.03."


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS