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Consider a triangle ABC right-angled at B in which the side BC = 9 and the angle α = 30° (α being the angle \(\widehat{ABC}\)).

Using these information, can you calculate the lenghts AB and AC?

 

Good luck!

 Jan 13, 2016

Best Answer 

 #4
avatar+2498 
+5

it is a 30 60 90 triangle: x,x sqrt(3),2x

60 is the opossite of 9 (x sqrt(3))

9/sqrt(3) = 5.1961524227066319 or 3sqrt(3) is opposite of 30 (x)

6sqrt(3) the opposite of 90 (2x)

 Jan 13, 2016
 #2
avatar+870 
0

Of course I am! (just kidding...)

"The world won't be destroyed by those who do evil, but by those who watch them without doing anything."

Albert Einstein

 Jan 13, 2016
 #4
avatar+2498 
+5
Best Answer

it is a 30 60 90 triangle: x,x sqrt(3),2x

60 is the opossite of 9 (x sqrt(3))

9/sqrt(3) = 5.1961524227066319 or 3sqrt(3) is opposite of 30 (x)

6sqrt(3) the opposite of 90 (2x)

Solveit Jan 13, 2016
 #5
avatar+129850 
0

..............

 Jan 13, 2016
edited by CPhill  Jan 13, 2016
 #6
avatar+870 
+5

Hint:

Pythagorus's theorem:

In any triangle right-angled at B, the lenght of the hypotenuse squared is equal to the sum of the squares of the lenghts of the two other sides” or, in other words:

AC²=AB²+BC²

 

Trigonometric functions:

In a right triangle, for any non-right angle α:

\(\sin(\alpha)=\frac{\text{opposite side}}{\text{hypotenuse}} \\\cos(\alpha)=\frac{\text{adjacent side}}{\text{hypotenuse}} \\\tan(\alpha)=\frac{\text{opposite side}}{\text{adjacent side}}\)

Respectively the sinus, the cosinus and the tangent of α.

 Jan 15, 2016

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