Explain how the Pythagorean Theorem is a special case of the Law of Cosines.

Track When rounding a curve, the acute angle $\theta$ that a runner's body makes with the vertical is called the angle of incline. It is described by the equation $\tan \theta=\frac{v^{2}}{g r},$ where $v$ is the velocity of the runner, g is the acceleration due to gravity, and r is the radius of the track. The acceleration due to gravity is a constant 9.8 meters per second squared. Suppose the radius of the track is 15.5 meters. Find the runner's velocity if the angle of incline is $13^{\circ}$.

The distance between Miami and Orlando is about 220 miles. A pilot flying from Miami to Orlando starts the flight $10^{\circ}$ off course to avoid a storm. If the pilot adjusts his course after 100 miles, how much farther is the flight than a direct route?

The distance between Miami and Orlando is about 220 miles. A pilot flying from Miami to Orlando starts the flight $10^{\circ}$ off course to avoid a storm. After flying in this direction for 100 miles, how far is the plane from Orlando?

Track When rounding a curve, the acute angle $\theta$ that a runner's body makes with the vertical is called the angle of incline. It is described by the equation $\tan \theta=\frac{v^{2}}{g r},$ where $v$ is the velocity of the runner, g is the acceleration due to gravity, and r is the radius of the track. The acceleration due to gravity is a constant 9.8 meters per second squared. Suppose the radius of the track is 15.5 meters. What is the runner's velocity if the angle of incline is $11^{\circ} ?$

Find $\csc 390^{\circ}$

Write each measure as a decimal to the nearest thousandth. $1002^{\circ} 30^{\prime} 30^{\prime \prime}$

For $\triangle M N P$ and $\triangle R S T, \angle M \cong \angle R, \angle N \cong \angle \mathrm{S},$ and $\angle P \cong \angle T$. Use the Law of sines to show $\triangle M N P \sim \triangle R S T$.

Find all solutions for each triangle. If no solutions exist, write none. Round to the nearest tenth. $b=40, a=32, A=125.3^{\circ}$

Latasha and Markisha are flying kites on a windy spring day. Latasha has released 250 feet of string, and Markisha has released 225 feet of string. The angle that Latasha's kite string makes with the horizontal is $35^{\circ} .$ The angle that Markisha's kite string makes with the horizontal is $42^{\circ} .$ Which kite is higher and by how much?

Find the values of the six trigonometric functions for each angle $\theta$ in standard position if a point with the given coordinates lies on its terminal side. $(8, -2)$

A landscaper wants to plant begonias along the edges of a triangular plot of land in Winton Woods Park. Two of the angles of the triangle measure $95^{\circ}$ and $40^{\circ} .$ The side between these two angles is 80 feet long. What is the perimeter of this triangular plot of land?

A landscaper wants to plant begonias along the edges of a triangular plot of land in Winton Woods Park. Two of the angles of the triangle measure $95^{\circ}$ and $40^{\circ} .$ The side between these two angles is 80 feet long. Find the length of the other two sides of the triangle.

A landscaper wants to plant begonias along the edges of a triangular plot of land in Winton Woods Park. Two of the angles of the triangle measure $95^{\circ}$ and $40^{\circ} .$ The side between these two angles is 80 feet long. Find the measure of the third angle.