Exam 7: Triangles

A plane is flying with an airspeed of 243 miles per hour with heading 271.7°. The wind currents are running at a constant 44.7 miles per hour in the direction 261.6°. Find the ground speed and true course of the plane. Apply the rules regarding the use of significant digits after all computations are complete. __________ mph with heading __________°

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. ​

The area of a triangle is 80 in². Find the length of the side included between the angles  Round to three significant digits. b = __________ inches

For the triangle described below, solve for B and use the results to explain why the triangle has one solution.  ft,  ft

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. ​

A man standing near a radio station antenna observes that the angle of elevation to the top of the antenna is b ​ = 67°. He then walks 100 feet further away and observes that the angle of elevation to the top of the antenna is ​a ​ = 45° . Find the height of the antenna to the nearest foot. ( Hint : Find x first.)​ ​

Is the pair of vectors and  perpendicular? ​

For the triangle described below, solve for B . Apply the rules regarding the use of significant digits to each angle and length after all computations are complete.  ft,   ft ​

A hot-air balloon is held at a constant altitude by two ropes that are anchored to the ground. One rope is 125 feet long and makes an angle of 63° with the ground. The other rope is 115 feet long. What is the distance between the points on the ground at which the two ropes are anchored? Apply the rules regarding the use of significant digits to each angle and length after all computations are complete. ​

Use the law of cosines to show that, if , then .

Referring to triangle ABC, find the area of the triangle. ​ Round to three significant digits. S = __________ m²

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

Find all solutions to the triangle described below.  km,  km 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 )​ __________°   __________°   __________ km

A plane is flying with an airspeed of 170 miles per hour and heading of 150°. The wind currents are running at 36 miles per hour at 165° clockwise from due north. Use vectors to find the true course and ground speed of the plane. Apply the rules regarding the use of significant digits after all computations are complete. __________ mph with heading __________°

The problem that follows refers to triangle ABC .​ If  and  cm, find C  and a . Apply the rules regarding the use of significant digits after all computations are complete. __________° ​ __________ cm

The problem that follows refers to triangle ABC . ​ If  and  km, find C  and c Apply the rules regarding the use of significant digits after all computations are complete. ​

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

Referring to triangle ABC, find the area of the triangle. ​ Round to three significant digits. S = __________ m²

The information below refers to triangle ABC . ​ Apply the rules regarding the use of significant digits after all computations are complete. Find A , b , and c . __________° ​ __________ cm ​ __________ cm

For the pair of vectors, find  .   ​