Name: Period: Geometr Honors Unit 5: Trigonometr Homework Section 5.1: Pthagorean Theorem Find the value of each variable or missing side. Leave answers in simplest radical form ND as a decimal rounded to the hundredths place. 1. 2. 3. 60ft. 2 in 3 in 1 50ft 3 a 1 5. 6... 13in 1in 20 b 16 22. a =, b=. a =, b = 11. a = 6, c =. a = 3, b = The numbers represent the lengths of the sides of a triangle. lassif each triangle as acute, obtuse, or right. 13. 6,, 1. 1, 2, 30. 20, 0, 1 16., 2, 25 1. 2, 5, 6 nswer each word problem. Round each solution to the nearest hundredth. Draw a picture to help ou. 1. The bottom of a ladder must be placed 3 feet from a wall. The ladder is feet long. How far above the ground does the ladder touch the wall? 1. How far from the base of the house do ou need to place a -foot ladder so that it eactl reaches the top of a - foot tall wall? 20. suitcase measures 2 inches long and 1 inches high. What is the length from corner to corner? REVIEW: Simplif. Leave answers as simplified radicals. 1. 2. 3. 3 3 HOW TO for the REVIEW 1. Multipl the top and the bottom b the radical in the bottom 2. Simplif the radical in the bottom (Remember = = ) 3. Reduce the fraction if possible
Section 5.2: Special Right Triangles Find the value of the variable. Leave answers in simplest radical form. 1. 2. 3.. d 25 1 a c b 5. 6... 2 z.. s 11.. 30 3 s 6 s 2 s 5 Honors Onl! Find the value of each variable. 13. 5 1.. p r a q 2 3 s b w z 5 REVIEW: Identif whether each line is a midsegment, altitude, angle bisector, perpendicular bisector, or median. 1. 2. 3. R. 5. F O D D E P Q L E
Section 5.3: Sine, osine, and Tangent Find the value of. Round answers to the hundredths place. 1. 2. 65 3.. 62 2 3 3 5. 6 6... 0 55 2 20 55 5.. 11.. 13 5 0 32 w 1 33 13. 1.. 16. w 1.3 2 5. 2 55 33 3 1 1. n escalator at a shopping center is 200 ft long, and rises at an angle of º. What is the vertical rise of the escalator to the nearest tenth of a foot? 1. -ft-long ladder is leaning against a wall and makes a 6º angle with the ground. How high does the ladder reach on the wall? Round to the nearest inch. 20. straight ramp rises at an angle of 25.5º and has a base 30 ft long. How high is the ramp? Round to the nearest foot. REVIEW: MY, PX, and NZ are medians. 1. Find the measure of WY if MW = 22. 2. What is NW if ZW =? 3. If PW = 13, what is WX? M Z X W Y N
Section 5.: Finding ngles Using Trig Find the value of each variable. Round to the nearest hundredth..5 1. 1 2. 3.. 2 2 6 1 1 5. 6... 5 1 1.. 11.. 3 5 6.5 13. 1.. 1 16. 30 2 20 1 1 16 Review: Draw a diagram to help solve each problem. 1. tree 2 feet tall casts a shadow feet long. Ma is 6 feet tall. How long is Ma's shadow? 2. model plane has a scale of 1 in : 6 d. If the model plane is 5.6 in tall then how tall is the real plane? 3. ft tall statue standing net to an adult elephant casts a 1 ft shadow. If the adult elephant is ft tall then how long is its shadow?
Section 5.5: ngles of Elevation and Depression Find the value of. Round the lengths to the nearest hundredth. 1. 2. 3.. 5. 6. Draw a diagram to find the missing value. Round to the nearest hundredth.. person is standing 0 ft from a flagpole and can see the top of the pole at a 35º angle of elevation. The person s ee level is ft from the ground. What is the height of the flagpole?. n eagle perched 0 ft up in a tree looks down at a 35º angle and spots a vole. How far is the vole from the eagle?. You stand 0 ft from a tree. The angle of elevation from our ees (5 ft above the ground) to the top of the tree is º. How tall is the tree?. n airplane is fling at an altitude of,000 ft. The airport at which it is scheduled to land is 50 mi awa. Find the average angle at which the airplane must descend for landing. 11. lake measures 600 ft across. lodge stands on one shore. From our point on the opposite shore, the angle of elevation to the top of the lodge is º. How high above the lake does the lodge stand?. librar needs to build an access ramp for wheelchairs. The main entrance to the librar is ft above sidewalk level. If the architect designs the slope of the ramp in such a wa that the angle of elevation is 5º, how long must the access ramp be?
Section 5.6: Law of Sines and osines Find each of the following using the law of sines or cosines. Round to the nearest hundredth. 1. 2. 63 22 33 2 3.. 21 0 32 1 23 2 5. Draw XYZ with = 1, m X = 2, m Y =, and m Z = 1. Then find the length of side z to the nearest whole number. 6. The sides of a regular heagon measure centimeters. Each interior angle measures 0. Find the length of segment F, in heagon DEF to the nearest centimeter.. Marker and Marker are miles apart. Marvin walks 1. miles from Marker and realizes that he is 6 degrees offcourse. To the nearest tenth of a mile, how far from Marker is Marvin when he realizes his error?. James and Regina are standing at the seashore miles apart. The coastline is a straight line between them. oth James and Regina can see the same ship in the water. The angle between the coastline where James is standing and the ship is 35 degrees. The angle between the coastline where Regina is standing and the ship is 5 degrees. How far is the ship from James?. Terrell, Devon, and Henr are sleeping in their camping tents. The distance between Terrell and Devon is 3 feet. The distance between Terrell and Henr is 201 feet. The distance between Devon and Henr is 15 feet. If Devon walks out of his tent, he can see both tents. t what angle can Devon see both Terrell s and Henr s tents?. Find all of the missing sides and angles. FG = D ED = EF = m G = m FDG = 20 m EDF = m DFE = E 30 5 F G
Unit 5 Practice Test Find the eact value of each side. Epress in simplest radical form. ircle our answers. [5 points each] 1. 2. 3.. Find the missing side to the nearest hundredth. [5 points each] 5. 6. 6.. 0 2 2 5 w Find the missing angle to the nearest hundredth. [5 points each]. 1..5 11.. 5 1 Draw a diagram to solve each problem. [5 points each: 2 points for the diagram, 3 points for the correct answer] 13. Twent minutes after being launched, a hot-air balloon has risen to an altitude of 00 ft. The pilot can still see the starting point on the ground at a 50 angle of depression. How man feet is the balloon from the starting point? 1. 20 ft ladder leans against a wall at an angle of elevation of 33. How high up the wall does the ladder rest?. n airplane is fling at an altitude of 5,000 ft. The airport at which it is scheduled to land is 0 mi awa. Find the average angle at which the airplane must descend for landing. (1 mile = 520 feet) Solve for. Leave answers as simplified radicals. 16. 1. 1. 1. Find all missing sides and angles. 20. triangular plaground has sides of lengths 5 feet, 55 feet, and 01 feet. Find all angles. 2 21. Towers and are located miles apart. fire ranger spots a fire at a 2 from tower. nother fire ranger spots the same fire at a 6 from tower. To the nearest tenth of a mile, how far from tower is the fire? FIRE! 2 6 miles