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In triangle CAT, a=4, c=5, and Cos T=1/8. What is the length of t?
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In the triangle CAT, the angle T which is denoted by`/_T`
is adjacent to the sides a and c
As the side c is opposite to the `/_C` ,we can draw a perpendicular to the side c from `/_C`
Then we can create a right angle trinagle with side a as the hypotenuse and the perpendicular line is denoted by t'` `
The other two side of this new right angle triangle are a and c'
Then we can write,
`cos T =(c')/(a) =(1)/(8)`
as a = 4, c' = 1/2
by using the pythogoras theorm,
`t'^(2) =a'^(2) -c'^(2)`
`t'^(2) = 4^(2) -(1)/(2)^(2)`
`t' = sqrt(63)/2`
Then in the CAT triangle when we created a right angle triangel by drawing t' we have created another right angle triangle with side t as the hypotenuse
we can apply the pythogoras theorm to that right angle side as well
`t^(2) = t'^(2) + (c-c')^(2)`
`t^(2) = (63)/(4) + (5 -(1)/(2))^(2)`
`t^(2) = (63/4) + ( 9/2)^(2)`
`t^(2) = (63/4) + (81/4)`
`t^(2) = (144/4)`
t = 6
Posted by malagala on May 15, 2012 at 5:00 AM (Answer #1)
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