Trigonometry

A ladder $10$ m long leans against a vertical wall. The angle $\theta$ between the ladder and the level ground has $\cos\theta = 0.6$. How many metres is the foot of the ladder from the wall?

Convert $\dfrac{3\pi}{4}$ radians to degrees.

What is $\sin 120^\circ$?

Which expression equals $\sin 75^\circ$?

In triangle $ABC$, $a = 5$, $b = 8$ and the angle $C$ between them is $60^\circ$. Find $c$.

Our proof of the law of cosines puts $C$ at the origin, $B = (a, 0)$ and $A = (b\cos C, b\sin C)$. Why does the proof also work when the angle $C$ is obtuse?

How many angles $x$ with $0^\circ \le x < 720^\circ$ satisfy $\sin x = 0.3$?

Compute $8 \sin 10^\circ \sin 50^\circ \sin 70^\circ$ exactly. (Hint below if you need it.)

Which Lean statement says correctly that $\sin(\alpha + \beta) = \sin\alpha + \sin\beta$ is not an identity?

Write third_side(a, b, angle_c_degrees) that returns the side $c$ of a triangle with sides $a$, $b$ and the angle $C$ between them given in degrees, using the law of cosines. Remember that math.cos expects radians.