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The sides of a rectangle are 1 and 3, and its diagonals intersect forming an angle of \(\theta.\) Find \(\sin \theta\)

 Sep 20, 2019
 #1
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Around 36.87 degrees.

 Sep 20, 2019
 #2
avatar+109334 
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The diagonal length will be  √ [1^2 + 3^2] =  θ

 

The sin of (1/2)θ  = (1.5)/ [√ [10] /2  ]  =  3/√ 10

And the coc of (1/2) θ = .5 /  [ √ [10 ] / 2 ]  =  1/ √ 10

 

So

 

sin [2 (1/2)θ]  = sin(θ)  =  2 (3)(1) / ( √ 10)^2  =    6/10   =    3/5

 

 

cool cool cool

 Sep 20, 2019
edited by CPhill  Sep 20, 2019

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