Name:AlgebraII12.1 WorksheetPeriod:9.1 Introduction to TrigNameGETTIN' TRIGGY WIT ITSOHFind the following ratios using the given right triangles.1.CAHTOA2.Sin A Sin B Sin A Sin B Cos A Cos B Cos A Cos B Tan A Tan B Tan A Tan B Use your calculator to evaluate each of the following. Round each to four decimal places.3. sin 63 4. cos24 5. tan 86 Use the tangent ratio to find the variable.7.8.9.Use the sine ratio to find the variable.10.11.12.Use the cosine ratio to find the variable.18.104.22.168. tan 42
Solve the following right triangles. (Find all of the missing sides and angles.)22.214.171.124.20.21.
Name: Period:9.2 Trig Ratios in DilationsUse your calculator to calculate each ratio usingthe ANGLE of A and B.Make sure you are in degree mode.sin A sin B 1. Use the diagram below as two legs of a right trianglea) Draw a hypotenuse- make it different than any studentaround you.b) Measure & label the two other angles A, B in your diagram.Use your angles to complete this table A:cos A cos B tan A tan B How are 𝐴 𝑎𝑛𝑑 𝐵 related to each other?Use your fractions to calculate each ratio usingthe ratios (SOH CAH TOA) that define each trigfunction. Round to three decimals placessin A sin B c) Measure all 3 sides of the triangle in cm to the tenths place.Label triangle with measurements.d) Use your measured side lengths to find the ratios for sine,cosine and tangent. Record in the table B.Put Asomewhereonthislinecos A cos B tan A tan B Put B somewhere on this line2. DILATE. Using point M as the center of dilation, dilateΔABC above. The dilation will cover the words, it’s ok.What is your scale factor?Draw the dilationUse your calculator to calculate each ratio usingthe ANGLE of A’ and B’.sin A’ sin B’ cos A’ cos B’ b) Measure & label 𝐴′ 𝑎𝑛𝑑 𝐵′ in your dilation. Use yourangles to complete the table C:How are 𝐴′ 𝑎𝑛𝑑 𝐵′ related to the angles in ΔABC?tan A’ tan B’ c) Measure all 3 sides of the dilated triangle in cm to thetenths place. Label dilated triangle with measurements.d) Use your measured side lengths to find the ratios for sine,cosine and tangent table D.How did your tables compare to each other and to theoriginal table?Use your calculator to calculate each ratio usingthe ratios (SOH CAH TOA) that define eachtrig function for your dilated triangle.sin A’ sin B’ cos A’ cos B’ tan A’ tan B’
43. In ΔCAT, find the ratio for sin C, and the cos T. What do you notice?Find another angle pair whose trig functions are equalWhy does that happen? 4. You can use the sin-1 cos-1 and tan -1 buttons on your calculator to find the unknown angle if sides ofthe triangles are known. Make sure you are in degree mode. Label the sides of the triangle with“hypotenuse opposite or adjacent” to help you determine which trig function to use.Round to tenths place. Show your work.For example:𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒since 𝑡𝑎𝑛𝑔𝑒𝑛𝑡 𝜃 �𝑒𝑛𝑡you can use 𝑡𝑎𝑛 1 ( 𝜃 𝑎𝑛𝑑 𝜃 50
Name class9.3 Word Problems using Right TrianglesStrategy:What1. Suppose you have been assigned to measure the height of the local water tower.Climbing makes you dizzy, so you decide to do the whole job at ground level.From a point 47.3 meters from the base of the water tower, you find that you mustlook up at an angle of 53 to see the top of the tower. How tall is the tower? Drawthe triangle.2. A ship is passing through the Strait of Gibraltar. At its closest point of approach,Gibraltar radar determines that it is 2400 meters away. Later, the radar determinesthat it is 2650 meters away. By what angle did the ship’s bearing from Gibraltarchange? How far did the ship travel during the two observations?3. You lean a ladder 6.7 meters long against the wall. It makes an angle of 63 withthe level ground. How high up is the top of the ladder?4. You must order a new rope for the flagpole. To find out what length of rope isneeded, you observe that pole casts a shadow 11.6 meters long on the ground. Theangle between the sun’s rays and the ground is 36.8 . How tall is the pole?
5. Your cat is trapped on a tree branch 6.5 meters above the ground. Your ladder isonly 6.7 meters long. If you place the ladder’s tip on the branch, what angle willthe ladder make with the ground?6. The tallest free standing structure in the world is the 553 meter tall CN tower inToronto, Ontario. Suppose that at a certain time of day it casts a shadow1100meters long on the ground. What is the angle of elevation of the sun at that time ofday?7. Scientists estimate the heights of features on the moon by measuring the lengthsof the shadows they cast on the moon’s surface. From a photograph, you find thatthe shadow cast on the inside of a crater by its rim is 325 meters long. At the timethe photograph was taken, the sun’s angle to the horizontal surface was 23.6 . Howhigh does the rim rise above the inside of the crater?8. A beam of gamma rays is to be used to treat a tumor known to be 5.7 cmbeneath the patient’s skin. To avoid damaging a vital organ, the radiologist movesthe source over 8.3 cm. At what angle to the patient’s skin must the radiologist aimthe gamma ray source to hit the tumor? How far will the gamma rays haveto pass through the body to hit the tumor?
Name:Period:9.4 Clinometer measurement activityIntroduction:In this activity you will use trigonometry to make indirect measurements todetermine the heights of tall objects. At the end of the lab, we will use the entireclass’ data to come up with a reasonably accurate measurement of the flagpole.The diagram on the right is to be used as a template. The distance D should bemeasured (along the ground) to your tall object. The clinometer should be used tomeasure the angle 𝛼. The length E, the height to your eyes, should be measured aswell.Part 1: Measuring your first object – Pick any tall object on campus and determine its height.Object being measured:Draw a diagram of the right triangle, labeling the angle, and length clearly. Please show all calculations.Diagram WorkPart 2: Measuring your second object – Pick any tall object on campus and determine its height.Object being measured:Draw a diagram of the right triangle, labeling the angle, and length clearly. Please show all calculations.Diagram WorkUnderstanding check: Explain why you must always use the tangent for these measurements:Please double check your work with the teacher or your classmates before proceeding to part 3
Part 3: Measuring the flag poleFor this measurement we want to be more precise than parts 1 and 2. To make sure you are more accurate, you will taketwo measurements. You will measure in feet and inches. Make sure you properly convert inches to decimals(5′8" 5.8)Measurement 1:Measure the angle from some distance away.Distance:Angle:Diagram WorkMeasurement 2:Measure the angle from a distance further away.Distance:Angle:Diagram WorkUse the average of your 2 values to determine the height of the flagpole:Flagpole height (averaged):Now, let’s use statistics to get an average of the class’ data. Get data from your classmates and put their averaged flagpoleheight in the table below.Q1. What is the average (arithmetic mean) of the class’ data?Q2. Construct a box and whisker plot of the data. How does your measurement compare to the class’ data?
Name: Period:9.5 Three Trig Towers!Round to the tenths place at each step. Figures not drawn to scale (do not measure).Use trig ratios to solve for lengths of the triangles as needed to end up solving for X. Show your work.#1START43010520XSTART32#22.5X
Name class9.6 Review Unit 9Use the diagram at the right. Find each of the following. Leave answers as fractions.1) sin C 2) cos C 3) sin T 4) tan T For questions 5 & 6, give your answer to the nearest 0.001.5) sin T 6) cos T Solve, round to the nearest hundredth.7) cos 640 𝑥28x 8) tan 510 14.8𝑥𝑥 9) find w 10) Find x 11. Solve for Θ 12) Solve for Θ and 𝐴𝐵And 𝐴𝐶
For each question draw & label a picture, solve for the missing part.13. A ladder 7 m long stands onlevel ground and makes a 730angle with the ground and restsagainst a wall. How far from thewall is the base of the ladder?14. To see the top of a building1000 feet away, you look up to240 from the horizontal. What isthe height of the building?15. A guy wire is anchored 12feet from the base of a pole. Thewire makes a 58o angle with theground. How long is the wire?16. A submersible traveling at adepth of 250 feet dives at anangle of 15º with respect to a lineparallel to the water’s surface. Ittravels a horizontal distance of1500 feet during the dive. Whatis the depth of the submersibleafter the dive?17. Brothers Bob and Tom Katzbuy a tent that has a center pole6.25 feet high. If the sides of thetent are supposed to make a 50 angle with the ground, how wideis the tent?18. A swimming pool is 30meters long and 12 meters wide.The bottom of the pool is slantedso that the water depth is 1.3meters at the shallow end and 4meters at the deep end. Find theangle of depression of the bottomof the pool.
original table? Use your calculator to calculate each ratio using of A and B. Make sure you are in degree mode. sin A sin B cos A cos B tan A tan B Use your fractions to calculate each ratio using the ratios (SOH CAH TOA) that define each trig function. Round to three decimals places sin A sin B cos A cos