Exam 7: Triangles

For the triangle described below, solve for B and use the results to explain why the triangle has no solution.  ft,  ft

Consider the triangle described below. yd,  yd Apply the rules regarding the use of significant digits to each angle and length after all computations are complete. How many different possible triangles are there? __________ ( no solution / two solutions / one solution )​ __________°   __________°   __________ yd

The information below refers to triangle ABC .  inches. Find all the missing parts. Apply the rules regarding the use of significant digits after all computations are complete. ​

Solve the triangle. yd, yd, yd ​ Apply the rules regarding the use of significant digits after all computations are complete. __________° ​ __________° ​ __________°

Draw the vector V  that goes from the origin to the given point. Then write V  in component form ​ ​

A plane headed due south is traveling with an airspeed of 180 miles per hour. The wind currents are moving with constant speed in the direction 30°. If the ground speed of the plane is 90 miles per hour, what is its true course? True course: __________°

Find the angle θ  between the given vectors to the nearest tenth of a degree. ​

Find the magnitude of the vector.

A man is flying in a hot-air balloon in a straight line at a constant rate of 6 feet per second, while keeping it at a constant altitude. As he approaches the parking lot of a market, he notices that the angle of depression from his balloon to a friend's car in the parking lot is 36°. A minute and a half later, after flying directly over this friend's car, he looks back to see his friend getting into the car and observes the angle of depression to be 37°. At that time, what is the distance between him and his friend? (Give your answer to the nearest foot.) Distance = __________ ft

The area of a triangle is 70 in². Find the length of the side included between the angles Round to three significant digits.

Show that the pair of vectors  and  is perpendicular.

Referring to triangle ABC, find the area of the triangle. ​ Round to three significant digits. S = __________ inches²

Two ships leave a harbor entrance at the same time. The first ship is traveling at a constant 19 miles per hour, while the second is traveling at a constant 23 miles per hour. If the angle between their courses is 121°, how far apart are they after 2 hours? Apply the rules regarding the use of significant digits after all computations are complete.

A 50-foot wire running from the top of a tent pole to the ground makes an angle of 54° with the ground. If the length of the tent pole is 44 feet, how far is it from the bottom of the tent pole to the point where the wire is fastened to the ground? (The tent pole is not necessarily perpendicular to the ground.)Apply the rules regarding the use of significant digits to each angle and length after all computations are complete.​ __________ ft.

Two planes take off at the same time from an airport. The first plane is flying at 246 miles per hour on a course of 130.0°. The second plane is flying in the direction 165.0° at 359 miles per hour. Assuming there are no wind currents blowing, how far apart are they after 2 hours? Apply the rules regarding the use of significant digits after all computations are complete.

The circle in the figure below has a radius of r and center at C . The distance from A to B is x , the distance from A to D is y , and the length of arc BD is s . For the following problem, redraw the figure, label it with the values given, and then solve. ​ If  and  find x . Apply the rules regarding the use of significant digits after all computations are complete. ​ __________

For the pair of vectors, find , , and . ​   ​   ​

For the pair of vectors, find . ​

Find the magnitude of the vector.

Find the work performed when the given force F is applied to an object, whose resulting motion is represented by the displacement vector d. Assume the force is in pounds and the displacement is measured in feet. ​ Work = __________ ft-lb