please explain how you got the answer
Thank You!
Thank You!
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side opposite to the shortest angle is the shortest side
=> side opposite to angle 30 is shortest = 3root3
=> tan60 = x/(3root3).............where x is the side opposite to 60 degree ,that is, the second longest side.
=> root3 = x/(3root3)
=> x = 9 units
ans: second longest side = 9 units
=> side opposite to angle 30 is shortest = 3root3
=> tan60 = x/(3root3).............where x is the side opposite to 60 degree ,that is, the second longest side.
=> root3 = x/(3root3)
=> x = 9 units
ans: second longest side = 9 units
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30 60 90 triangles are all about ratios. If the shortest side (the side opposite the 30 degree angle) is 1, then the middle side is root 3, and the hypotenuse is 2. So therefore the middle side is root three times as big as the smallest side. Then we can just take the length of the shortest side that is given (3root3) and multiply it by this ratio (root3/1) and come out with 3(root3)(root3)=3(3)=9.
Hope I helped!
Hope I helped!
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The basic 30,60,90 triangle has sides 1,2,√3, with 2 of course being the hypotenuse............
So if the shortest side in such a triangle is 3√3, then the hypotenuse is 6√3 and the remaining side is 3√3 x √3 = 9.
You can also do it the hard way:
√[(6√3)^2 - (3√3)^2] = √(108 - 27) = √81 = 9
So if the shortest side in such a triangle is 3√3, then the hypotenuse is 6√3 and the remaining side is 3√3 x √3 = 9.
You can also do it the hard way:
√[(6√3)^2 - (3√3)^2] = √(108 - 27) = √81 = 9
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the other 2 sides are 6root3 and 9......
Solution:If a,b and c be the sides of the triangle opposite to angles A,B and C,respectively then use the formula a/sinA =b/sinB =c/sinC....Put the values of A B and C as30 60 and 90 and u will get an expression as 2a=b=2c/root3 (if a is considered to be the shortest side,,taking angle A=30)..now putting a=3root3 u will get the values of b and c........njoy:-)
Solution:If a,b and c be the sides of the triangle opposite to angles A,B and C,respectively then use the formula a/sinA =b/sinB =c/sinC....Put the values of A B and C as30 60 and 90 and u will get an expression as 2a=b=2c/root3 (if a is considered to be the shortest side,,taking angle A=30)..now putting a=3root3 u will get the values of b and c........njoy:-)
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O.k. First thing you need to know is that in a triangle the largest angle will be opposite the largets side and thae smallest angle the smallest side.
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First, SinA/a=SinB/b=SinC/c where A is the angle and a is the side opposite to the angle. Same for the other letters. Since 3root3 is the smallest side then it is opposite to the smallest angle,30. And that for the second longest angle is 60.
Thus Sin60/x=Sin30/3root3 thus x= 9
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First, SinA/a=SinB/b=SinC/c where A is the angle and a is the side opposite to the angle. Same for the other letters. Since 3root3 is the smallest side then it is opposite to the smallest angle,30. And that for the second longest angle is 60.
Thus Sin60/x=Sin30/3root3 thus x= 9
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tan 60 ° = x / (3√3)
x = 3√3 tan 60 ° = 3√3 √3 = 9 is the shortest side.
x = 3√3 tan 60 ° = 3√3 √3 = 9 is the shortest side.
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It's 3root3 multiplied by root 3, which equals 9.