Exercises: Understand Trigonometric Ratios

Two triangles both have a 90° angle and a 35° angle. Which criterion guarantees they are similar?

Triangle $PQR$ is similar to triangle $STU$. Side $PQ = 6$, side $ST = 9$, and side $QR = 8$. What is side $TU$?

Right triangle $ABC$ has legs $AC = 5$ and $BC = 12$ and hypotenuse $AB = 13$. Right triangle $DEF$ is similar to $\triangle ABC$ with hypotenuse $DE = 26$. What is the ratio $\frac{EF}{DE}$ in triangle $DEF$? Express as a fraction.

In right triangle $ABC$ with a right angle at $C$, $BC = 3$, $AC = 4$, and $AB = 5$. What is $\sin(A)$? Express as a fraction.

Using the same triangle (sides 3, 4, 5 with right angle at $C$), what is $\cos(A)$? Express as a fraction.

Right triangle $XYZ$ has a right angle at $Z$, with $YZ = 5$, $XZ = 12$, and $XY = 13$. Which expression correctly gives $\tan(X)$?

Right triangle $PQR$ has a right angle at $R$, with $QR = 9$ and $PR = 4$. What is $\tan(P)$? Express as a fraction.

In right triangle $ABC$ with right angle at $C$, angle $A = 40\degree$ and $AB = 15$. Using $\sin(40\degree) \approx 0.643$, find the length of side $BC$. Round to the nearest hundredth.