InterviewSolution
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InterviewSolution
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In a triangle `ABC, (a)/(b) = (2)/(3) and sec^(2) A = (8)/(5)`. Find the number of triangle satisfying these conditions |
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Answer» Correct Answer - two We have `(a)/(b) = (b)/(3) = k` and `sec^(2) A = (8)/(5)` `rArr cos^(2) A = (5)/(8)` `rArr (5)/(8) = ((9k^(2) + c^(2) - 4k^(2))/(6kc))^(2) = ((5k^(3) + c^(2))/(6kc))^(2)` `rArr 45k^(2) c^(2) = 50 k^(4) + 20 k^(2) c^(2) + 2c^(4)` `rArr 2c^(4) - 25 k^(2) c^(2) + 50k^(4) = 0` `rArr c^(2) = (25 k^(2) +- sqrt(625 k^(4) - 400 k^(4)))/(4)` `= (25k^(2) +- 15 k^(2))/(4) = 10 k^(2), (5)/(2) k^(2)` There are two possible valid values of `c^(2)`. Hence there exist two triange satisfying the given conditions |
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