91Ó°ÊÓ

Angles play an important role in custom bikes that are properly fitted to the biking needs of cyclists. One of the angles to help find the perfect fit is called the hip angle. The figure indicates that the hip angle is created when you're sitting on the bike, gripping the handlebars, and your leg is fully extended. Your hip is the vertex, with one ray extending to your shoulder and the other ray extending to the front-bottom of your foot. The table indicates hip angles for various biking needs. Use this information to pedal through. $$ \begin{array}{|l|l|} \hline \text { Hip Angle } & \text { Used For } \\ \hline 85^{\circ} \leq \text { hip angle } \leq 89^{\circ} & \text { short- distance aggressive racing } \\ \hline 91^{\circ} \leq \text { hip angle } \leq 115^{\circ} & \text { long- distance riding } \\ \hline 116^{\circ} \leq \text { hip angle } \leq 130^{\circ} & \text { mountain biking } \\ \hline \end{array} $$ Which type or types of biking require an obtuse hip angle?

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Because a parallelogram can be divided into two triangles with the same size and shape, the area of a triangle is onehalf that of a parallelogram.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. If a polygon is not regular, I can determine the sum of the measures of its angles, but not the measure of any one of its angles.

Use a quadratic equation to solve this problem. The width of a rectangular carpet is 7 meters shorter than the length, and the diagonal is 1 meter longer than the length. What are the carpet's dimensions?

Describe what happens to the tangent of an angle as the measure of the angle gets close to \(90^{\circ}\).

From the top of a 250 -foot lighthouse, a plane is sighted overhead and a ship is observed directly below the plane. The angle of elevation of the plane is \(22^{\circ}\) and the angle of depression of the ship is \(35^{\circ}\). Find a. the distance of the ship from the lighthouse; b. the plane's height above the water. Round to the nearest foot.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I paid \(\$ 10\) for a pizza, so I would expect to pay approximately \(\$ 20\) for the same kind of pizza with twice the radius.

Sighting the top of a building, a surveyor measured the angle of elevation to be \(22^{\circ}\). The transit is 5 feet above the ground and 300 feet from the building. Find the building's height. Round to the nearest foot.

Describe the differences among lines, half-lines, rays, and line segments.

A rectangular swimming pool measures 14 feet by 30 feet. The pool is surrounded on all four sides by a path that is 3 feet wide. If the cost to resurface the path is \(\$ 2\) per square foot, what is the total cost of resurfacing the path?