The sides of a rectangle are 1 and 3, and its diagonals intersect forming an angle of \(\theta.\) Find \(\sin \theta\)
Around 36.87 degrees.
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
