Exam 2: Right Triangle Trigonometry

Find the exact value of cot 60°.

Calculate the tangent values for each value of x indicated in the sets of tables shown below. Determine which set of tables displays the correct values. Round all answers to the nearest tenth. ​

Refer to right triangle ABC with . ​ ​ If  mm and  mm, find B . ​Apply the rules regarding the use of significant digits when determining your answer. ​ __________

Vector  V  with magnitude   forms an angle with the positive  x -axis. Give the magnitude of the horizontal and vertical vector components of  V , namely   and  , respectively. Apply the rules regarding the use of significant digits when determining your answer. ​ __________ ​ __________

To further justify the Cofunction Theorem, use your calculator to find a value for each pair of trigonometric functions below. In each case, the trigonometric functions are cofunctions of one another, and the angles are complementary angles. Round your answers to four places past the decimal point. sin 23°, cos 67° ​

Right triangle ABC  has , , and . Use this information to find sin A . ​

In the figure, the distance from A to D is y , the distance from D to C is x , and the distance from C to B is h . ​ If , , and , find h , then x . Round each answer to the nearest whole number. ​

Solve the following problem. Be sure to make a diagram of the situation with all the given information labeled. A ship is anchored off a long straight shoreline that runs north and south. From two observation points 16 miles apart on shore, the bearings of the ship are N 28º E and S 50º E. What is the shortest distance from the ship to the shore? Apply the rules regarding the use of significant digits when determining your answer. Round to one decimal place. __________ mi

Refer to right triangle ABC with . ​ ​ If  mm and  mm, find B . Round the answer to the nearest whole number. ​

Solve the following problem. Be sure to make a diagram of the situation with all the given information labeled. The two equal sides of an isosceles triangle are each 46 centimeters. The base measures 30 centimeters. Apply the rules regarding the use of significant digits when determining your answers. Round to the nearest units. Find the height. __________ cm Find the measure of the two equal angles. __________º

Danny and Stacey have gone from the swing to the slide at the park. The slide is inclined at an angle  . Danny weighs 47.0 pounds. He is sitting in a cardboard box with a piece of wax paper on the bottom. Stacey is at the top of the slide holding on to the cardboard box. Find the magnitude of the force Stacey must pull with, in order to keep Danny from sliding down the slide. (We are assuming that the wax paper makes the slide into a frictionless surface, so that the only force keeping Danny from sliding is the force with which Stacey pulls.)Apply the rules regarding the use of significant digits when determining your answer. ​ __________ lb

Use the information given in the diagram to find A to the nearest degree. Suppose that   and  . ​

A helicopter makes a forced landing at sea. The last radio signal received at station C gives the bearing of the helicopter from C as  at an N 57.1º E altitude of 423 feet. An observer at C sights the helicopter and gives as 12.1º. How far will a rescue boat at A have to travel to reach any survivors at B (see the figure)? Apply the rules regarding the use of significant digits when determining your answer.  Round your answer to the nearest ten feet. Distance rescue boat travels = __________ ft

Refer to right triangle ABC with . Solve for all the missing parts using the given information. Round the number of degrees, the number of minutes, and the lengths of the sides to the nearest whole number. ​

Suppose the figure below is an exaggerated diagram of a plane flying above the earth. The plane is 5.05 miles above the earth and the radius of the earth is 4,000 miles. To each of your answers, apply the rules regarding the use of significant digits when determining your answer. Round the distance to the nearest miles and the angle to the nearest tenth of degree. How far is it from the plane to the horizon? __________ mi ​What is the measure of angle A ? __________ °

Refer to right triangle ABC with . Solve for all the missing parts using the given information. ​ ,   m Apply the rules regarding the use of significant digits when determining your answer. __________ ​ __________ m ​ __________ m

Solve the following problem. Be sure to make a diagram of the situation with all the given information labeled. Apply the rules regarding the use of significant digits when determining your answers. A boat travels on a course of bearing for 78.7 miles. How many miles north has the boat traveled? __________ mi How many miles west has the boat traveled? __________ mi

A satellite is circling 112 miles above the earth, as shown in the figure. When the satellite is directly above point B , angle A is found to be 76.6°. Use this information to find the radius of the earth. Round your answer to the nearest mile. ​ ​

Solve the problem. Be sure to make a diagram of the situation with all the given information labeled. The two equal sides of an isosceles triangle are each 44 centimeters. If the base measures 30 centimeters, find the height and the measure of the two equal angles. Round your answers to the whole numbers. ​

Use a calculator to find a value of θ  between 0° and 90° that satisfies the statement below. Write your answer in degrees and minutes rounded to the nearest minute. csc  θ = 5.3187 θ =  _____°_____'