Exam 2: Right Triangle Trigonometry

A 10-pound weight is lying on a sit-up bench at the gym. If the bench is inclined at an angle , there are three forces acting on the weight, as shown in Figure. N is called the normal force and it acts in the direction perpendicular to the bench. F is the force due to friction that holds the weight on the bench. If the weight does not move, then the sum of these three forces is 0. Find the magnitude of N and the magnitude of F .   ​

Find the exact value for csc 60°. ​

Change the following to decimal degrees. 45°33' ​

Mark pulls Allison and Mattie in a wagon by exerting a force of 25 pounds on the handle at an angle  with the horizontal. How much work is done by Mark in pulling the wagon  feet? ​ ​

Find θ  if θ  is between 0° and 90°. Round your answer to the nearest tenth of a degree. cot  θ = 0.7382 θ =  __________°

Find the exact value of sec 30°.

A 10-pound weight is lying on a sit-up bench at the gym. If the bench is inclined at an angle of , there are three forces acting on the weight. N is called the normal force and it acts in the direction perpendicular to the bench. F is the force due to friction that holds the weight on the bench. If the weight does not move, then the sum of these three forces is 0. Find the magnitude of N and the magnitude of F . Apply the rules regarding the use of significant digits when determining your answers. __________ lb ​ __________ lb

Given the magnitude of the horizontal and vertical vector components  and  of vector V , find the magnitude of V .   ​

In the diagram below, angle A is in standard position. Find sin A . ​ ​

A package is pushed across a floor for a distance of 60 feet by exerting a force of 45 pounds downward at an angle of  with the horizontal. How much work is done? ​

Use the Cofunction Theorem to fill in the blank so that the expression becomes a true statement. _____°

Solve the following problem. Be sure to make a diagram of the situation with all the given information labeled. An equilateral triangle (one with all sides the same length)has an altitude of 4.6 inches. Find the length of the sides. Apply the rules regarding the use of significant digits when determining your answer. Round to one decimal place. Length of sides = __________ in.

Complete each of the following tables. Round all answers to the nearest tenth.

Solve the problem. Be sure to make a diagram of the situation with all the given information labeled. A tree on one side of a river is due west of a rock on the other side of the river. From a stake 19 yards north of the rock, the bearing of the tree is S18.7°W. How far is it from the rock to the tree? Round to the nearest tenth of yards. ​

Use a calculator to find the following. Round your answer to four places past the decimal point. sin 25°30'

The circle in the figure has a radius of r and center at C . The distance from A to B is x . ​ If  and , find x . Round the answer to the nearest whole number. ​

The circle in the figure has a radius of r and center at C . The distance from A to B is x . ​ If  and , find r . Apply the rules regarding the use of significant digits when determining your answer. __________

A ship is  off course. If the ship is traveling at 11 miles per hour, how far off course will it be after 3 hours? ​

The horizontal and vertical components of the velocity of an arrow shot into the air are 15.0 feet per second and 29.0 feet per second, respectively. Find the velocity of the arrow. Apply the rules regarding the use of significant digits when determining your answer. Velocity of arrow = __________ ft/sec

Use a calculator to complete the table of sin and csc values and determine which of the tables below displays the correct values. (Be sure your calculator is in degree mode.)Round all answers to four digits past the decimal point. If you have a graphing calculator with table-building capabilities, use it to construct the tables.