November 14, Special Right Triangles Triangle Theorem: The length of the hypotenuse is times the length of a leg.

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1 November 14, Special Right Triangles Triangle Theorem: The length of the hpotenuse is times the length of a leg. 3. Find the missing measures. e) If BC = 14 inches, find AC if triangle ABC is a triangle Triangle Theorem: The length of the hpotenuse is twice the length of the shorter leg, and the length of the longer leg is times the length of the shorter side. e) Using the same triangle, find BC if AC = 8 inches. 4. Find the missing measures. e) Find and Find the missing measures. e) Find and e) Find and e) Find and

2 November 14, Find and. 7. Find Find and. SOH CAH TOA

3 5-1 Special Triangles In-Class Find the eact values of and For Eercises 7 9, use the figure at the right. 7. If a 11, find b and c. c B 60 a A 30 b C 8. If b 15, find a and c. 9. If c 9, find a and b. For Eercises 10 and 11, use the figure at the right. 10. The perimeter of the square is 30 inches. Find the length of B C. A B D 45 C

4 Name: Date: Period: Writing Trig Ratios Task 1. Construct a triangle with angles A = 30, B = 60, and C = 90. Make sure to label our triangle. 2. Measure each side of the triangle to the nearest tenth of cm. AB = BC = CA = 3. Find the following ratios (keeping them in fraction form): CB = AC CB = AB AC = AB 4. Divide out our ratios above and round them to two decimals.

5 5. Construct a triangle with angles A = 40, B = 50, and C = 90. Make sure to label our triangle. 6. Measure each side of the triangle to the nearest tenth of cm. AB = BC = CA = 7. Find the following ratios (keeping them in fraction form): CB = AC CB = AB AC = AB 8. Divide out our ratios above and round them to two decimals.

6 9. Compare our ratios to the ratios of the other students in the class. What do ou notice? 10. The following are three trig ratios: Sine (A) = legopposite of angle A Hpotenuse Cosine (A) = legadjacent of anglea Hpotenuse Tangent (A) = legopposite of angle A legadjacent of anglea 11. Go back to #1 and #3 and determine which ratio is the sine, cosine and tangent.

7 November 14, θ 15 Find all trig ratios for the given triangle: 5 θ 10 Find all trig ratios for the given triangle: 3 θ 9 Find all trig ratios for the given triangle: 6 z 25 Find all trig ratios for the given triangle:

8 November 14, Find all trig ratios for the given triangle: Use a Calculator to find the following: sin (27) = sin -1 (3/5) = cos(58) = cos -1 (17.5) = tan (81) = tan -1 (21/7) = Right Triangle Hpotenuse Pthagorean Theorem In a right triangle where a and b are the legs and c is the hpotenuse, a 2 + b 2 = c 2 Leg Right Angle Leg a b c

9 SecondarMath2 Name 532SimilarTrianglesandTrigonometricRatios Period In3Class 1.WhatdoesSOH3CAH3TOAstandfor? Find%all%trigonometric%ratios%for%the%given%triangles.% % % Evaluate%using%a%calculator.%%Round%to%3%decimal%places.% 6.sin23 7.cos59 Find%all%the%trigonometric%ratios%for%the%given%angles.%% r 70 p FindallthetrigonometricratiosforBOTHanglesinthegivenrighttriangle:

10 November 14, 2013 e. Find the missing side in the right triangle using the pthagorean theorem: 3 4 e e. Find the missing side in the right triangle using the pthagorean theorem: 3 5 e e. Find the missing side in the right triangle using the pthagorean theorem: e. How to find trig in RIGHT triangles: SOH CAH TOA

11 November 14, 2013 Find: Find: sina= sinb= A sina= sinb= cosa= tana= csca= cosb= tanb= cscb= b C a c B cosa= tana= csca= cosb= tanb= cscb= seca= secb= seca= secb= cota= cotb= cota= cotb= Find: sina= Find: cosa= tana= sina= cosa= tana= csca= seca= cota=

12 November 14, 2013 Find the other si trigonometric functions: (hint: draw a triangle) Find the other si trigonometric functions: (hint: draw a triangle) Standing 12 ' from a tree ou must look up at 43 o to see the top of the tree. How tall is the tree? o A bird sitting on a 30 ' tower looks at a boat from an angle of depression of 55.5 o. How far is the boat from the tower?

13 SecondarMathII Name: 543RightTriangles Period: INCLASS Find%the%missing%side%length:% Draw%a%triangle%and%find%all%other%trigonometric%functions%for%problems%14:16:% % 6. 4 sinθ = tanθ = 12

14 Find%all%trigonometric%functions%for%problems%8:10:%

15 November 14, 2013 You want to hang up christmas lights on our house. There are bushes around our house, so the ladder has to be set up 5 feet awa from our house. If our roof is 21 feet tall, to the nearest foot, how tall does our ladder need to be? Draw a diagram. A moving truck is equipped with a ramp that etends from the back of the truck to the ground. When the ramp is full etended, it touches the ground 12 feet from the back of the truck. The height of the ramp is 2.5 feet. Draw a diagram then find the length of the ramp. Standing 15 ' from a tree ou must look up at 48 o to see the top of the tree. How tall is the tree? o A bird sitting on a 33 ' tower looks at a boat from an angle of depression of 50.5 o. How far is the boat from the tower?

16 November 14, 2013 A ship is just offshore of New York Cit. A sighting is taken of the Statue of Libert, which is about 305 feet tall. If the angle of elevation to the top of the statue is 30, how far is the ship from the base of the statue? You and our friends decide to sneak off one afternoon into the forbidden forest. You stumble into a clearing to avoid some star gazing centaurs and suddenl notice a large shadow, when ou look up at an angle of 35, ou see Grawp, Hagrid's giant brother. If Grawp is 27ft awa from ou, how tall is he? Ramps used for wheelchairs must have a ramp angle less than or equal to 8.33 degrees. The length of one ramp is 25 feet. The vertical rise is 18 inches. Estimate the ramp's horizontal distance and its ramp angle. A sonar operator on a ship detects a submarine at a distance of 400 meters and an angle of 35 degrees? How deep is the submarine? vertical rise length of ramp horizontal distance ramp angle 400 m

17 SecondarMath2 Name 534ContetualTrig Period INCLASS Drawapictureandusetrigonometricratiostosolve. 1.Theangleofelevationfromthebaseofawaterslidetothetopisabout13.Theslideetendshorizontall (alongtheground)about58.2meters.howtallistheslide? 2.Astandardbaseballdiamondisasquarewith90footsides.Howfarmustthefirstbasemanbeableto throwtogetsomeoneoutonthirdbase?giveanswertothenearesttenthofafoot. 3.Youarepaintingamuralonawall18feethigh.Sotheladderisstable,ismustbeplaced6feetawa fromthewall.tothenearestfoot,howtallmusttheladderbe? 5)DuringitsapproachtoEarth,thespaceshuttle sglideanglechanges.whenthespaceshuttleis5miles fromtherunwa,itsglideangleisabout19degrees.findtheshuttle saltitudeatthispointinitsdescent. Roundouranswertothenearesttenth. altitude glideangle runwa distancetorunwa

18 6) Aladder5mlong,leaningagainstaverticalwallmakesanangleof65 withtheground. a)howhighonthewalldoestheladderreach? b)howfaristhefootoftheladderfromthewall? c)whatangledoestheladdermakewiththewall? 9)Aballoonishovering800ftabovealake.Theballoonisobservedbthecrewofaboatasthelook upwardsatanangleof20degrees.twentjfivesecondslater,thecrewhastolookatangleof65degrees toseetheballoon.howfastwastheboattraveling? 10)Anairplaneclimbsatanangleof11 withtheground.findthegrounddistanceithastraveledwhenit hasattainedanaltitudeof400feet.

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