Exam 7: Triangles

Referring to triangle ABC, find the area of the triangle. ​ Round to three significant digits. S = __________ cm²

Draw the vector V  that goes from the origin to the given point. Then write V  in terms of the unit vectors i  and j .    ​

A tightrope walker is standing still with one foot on the tightrope as shown in the figure. If the tightrope walker weighs 124 pounds, find the magnitudes of the tension in the rope toward each end of the rope. Apply the rules regarding the use of significant digits after all computations are complete. ​a ​ = 75.5​,  ​b ​ = 81.5 ​ ​ __________ lbs ​ __________ lbs

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

Find the magnitude of the vector.

Draw a vector representing the course of a ship that goes  miles on a course with direction . ​

Find the magnitude of the vector.   ​

A ship is headed due north at a constant 14 miles per hour. Because of the ocean current, the true course of the ship is 12°. If the currents run at a constant 12 miles per hour, in what direction are the currents running? Apply the rules regarding the use of significant digits after all computations are complete. Angle(s)of current: __________°

Consider the triangle described below.  cm,  cm 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 )​ __________°   __________° ​   __________ cm

The information below refers to triangle ABC . ​ If  m, find A , b , and c . __________° ​ __________ m ​ __________ m

The diagonals of a parallelogram are 24 meters and 40 meters and intersect at an angle of 60°. Find the length of the longer side. ​

Find all solutions to the triangle described below.  inches,  inches ​Apply the rules regarding the use of significant digits to each angle and length after all computations are complete. ​

​For the pair of vectors, find  .   ​

A woman entering an outside glass elevator on the ground floor of a hotel glances up to the top of the building across the street and notices that the angle of elevation is 50°. She rides the elevator up three floors (70 feet)and finds that the angle of elevation to the top of the building across the street is 34°. How tall is the building across the street? (Give your answer to the nearest foot.) Height of building = __________ ft

Refer to triangle ABC . If cm, cm, and cm, find the largest angle. Apply the rules regarding the use of significant digits after all computations are complete. ​

The information below refers to triangle ABC . If   inches, find B , a , and b . Apply the rules regarding the use of significant digits after all computations are complete. __________° ​ __________ inches ​ __________ inches

A ship is anchored off a long straight shoreline that runs north and south. From two observation points 20 miles apart on shore, the bearings of the ship are N 28° E and S 53° E. What is the distance from the ship to each of the observation points? Apply the rules regarding the use of significant digits after all computations are complete.

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

A 140-foot antenna is on top of a tall building. From a point on the ground, the angle of elevation to the top of the antenna is 27.5°, while the angle of elevation to the bottom of the antenna from the same point is 22.5°. How tall is the building? (Give your answer to the nearest foot.) Height of building = __________ ft

Use the law of cosines to find a true statement from the list below, if . ​