2. Trigonometric Functions on Right Triangles

Solve each problem. See Examples 1 and 2. Distance Traveled by a Ship A ship travels 55 km on a bearing of 27° and then travels on a bearing of 117° for 140 km. Find the distance from the starting point to the ending point.

In circle O, if arc AB measures $48°$, what is the measure of angle CAB, where C is a point on the circle such that angle CAB is an inscribed angle that intercepts arc AB?

Solve each problem. (Source for Exercises 49 and 50: Parker, M., Editor, She Does Math, Mathematical Association of America.) Find a formula for h in terms of k, A, and B. Assume A < B.

Concept Check Suppose that ―90° < θ < 90° .   Find the sign of each function value. cos(θ―180°)

Use identities to solve each of the following. Rationalize denominators when applicable. See Examples 5–7. Find csc θ , given that cot θ = ―1/2 and θ is in quadrant IV.

An equation of the terminal side of an angle θ in standard position is given with a restriction on x. Sketch the least positive such angle θ , and find the values of the six trigonometric functions of θ . See Example 3. x = 0 , y ≥ 0

Given a right triangle with angle $\mathrm{FGE}$ and the side opposite to $\mathrm{FGE}$ has length $a$, the side adjacent to $\mathrm{FGE}$ has length $b$, and the hypotenuse has length $c$, which equation can be used to find the measure of angle $\mathrm{FGE}$?

In right triangle $PQR$, if angle $Q$ is the right angle, side $PQ$ = $7$ and side $QR$ = $8$, what is the measure of angle $R$? Round to the nearest degree.

In right triangle $△PQR$, the angle bisector of $\angle PQR$ is $QE$. If $m\angle PQE=20°$, what is the measure of $\angle PQR$?

In Exercises 1–8, use the Pythagorean Theorem to find the length of the missing side of each right triangle. Then find the value of each of the six trigonometric functions of θ.

Given a right triangle EGF with $\angle G$ as the right angle, if the side opposite $\angle E$ is $7$ units and the side adjacent to $\angle E$ is $9$ units, which is the best approximation for the measure of $\angle EGF$?

If an angle in a right triangle measures $x$ degrees, what is the measure of its supplement?

Given a right triangle $ABC$ and its translated image $A\text{'}B\text{'}C\text{'}$, which of the following statements is true?

Which of the following statements about $\mathrm{secants}$ and $\mathrm{chords}$ in a $\mathrm{right}\mathrm{triangle}$ is true?

In right triangle QRS, if angle $Q$ is the right angle and side $QR$ has length $6$ and side $QS$ has length $10$, what is the value of $\sin \left(S\right)$?