A triangle has two sides of lengths $5$ and $8$ with an angle of $3 0^{\circ}$ between them. What is its area?

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The angle $θ$ is acute and $sin θ = \frac{3}{5}$ . What is the value of $sin 2 θ$ , where $sin 2 θ = 2 sin θ cos θ$ ?
How many solutions does $2 sin^{2} x - sin x - 1 = 0$ have in the interval $0 \leq x < 2 π$ ?
How many solutions does $sin x = \frac{1}{3}$ have in the interval $0 \leq x \leq 4 π$ ?
It is given that $sin x + cos x = \frac{1}{2}$ . What is the value of $sin x cos x$ ?
What is the minimum value of $5 sin^{2} x + 2 cos^{2} x$ for real $x$ ?
It is given that $tan x = 2$ and $x$ is acute. What is $sin^{2} x$ ?