2EXAMPLE 1Find sine ratiosFind sin S and sin R. Write each answer as a fraction and as a decimal rounded to four places.SOLUTION=opp. Shypsin S=RTSR=63650.9692=opp. Rhypsin R=STSR=16650.2462
3GUIDED PRACTICEfor Example 1Find sin X and sin Y. Write each answer as a fraction and as a decimal. Round to four decimal places, if necessary.8170.4706,ANSWERor150.8824350.6,ANSWERor40.8
4EXAMPLE 1Find sine ratiosFind Sin A and Sin B. Write each answer as a fraction and as a decimal rounded to four places
5EXAMPLE 2Find cosine ratiosFind cos U and cos W. Write each answer as a fraction and as a decimal.SOLUTION=adj. to Uhyp=UVUW=1830=35cos U==adj. to Whyp=WVUW=2430=45cos W=
6EXAMPLE 3Use a trigonometric ratio to find a hypotenuseDOG RUNYou want to string cable to make a dog run from two corners of a building, as shown in the diagram. Write and solve a proportion using a trigonometric ratio to approximate the length of cable you will need.
7Use a trigonometric ratio to find a hypotenuse EXAMPLE 3Use a trigonometric ratio to find a hypotenuseSOLUTIONsin 35o=opp. hyp.Write ratio for sine of 35o.sin 35o=11xSubstitute.x sin 35o=Multiply each side by x.x =11sin 35oDivide each side by sin 35o.x110.5736Use a calculator to find sin 35o.x19.2Simplify.ANSWERYou will need a little more than 19 feet of cable.
8GUIDED PRACTICEfor Examples 2 and 3In Exercises 3 and 4, find cos R and cos S. Write each answer as a decimal. Round to four decimal places, if necessary.ANSWER0.6, 0.8ANSWER0.8824,In Example 3, use the cosine ratio to find the length of the other leg of the triangle formed.5.ANSWERabout 15.7 ft
9Find cos P and cos R. Write each answer as a fraction and as a decimal EXAMPLE 2Find cosine ratiosFind cos P and cos R. Write each answer as a fraction and as a decimal
11EXAMPLE 4Find a hypotenuse using an angle of depressionSKIINGYou are skiing on a mountain with an altitude of 1200 meters. The angle of depression is 21o. About how far do you ski down the mountain?
12Find a hypotenuse using an angle of depression EXAMPLE 4Find a hypotenuse using an angle of depressionSOLUTIONopp. hyp.=sin 21oWrite ratio for sine of 21o.1200x=sin 21oSubstitute.x sin 21o=Multiply each side by x.x =1200sin 21oDivide each side by sin 21ox12000.3584Use a calculator to find sin 21ox3348.2Simplify.ANSWERYou ski about 3348 meters down the mountain.
13GUIDED PRACTICEfor Example 4Suppose the angle of depression in Example 4 is 28°. About how far would you ski?6.WHAT IF?ANSWERabout 2556 m
14EXAMPLE 4Find a hypotenuse using an angle of depressionA pilot is looking at an airport from her plane. The angle of depression is 29 degrees. If the plane is at an altitude of 10,000 feet, approximately how far is it from the airport?
15EXAMPLE 5Find leg lengths using an angle of elevationSKATEBOARD RAMPYou want to build a skateboard ramp with a length of 14 feet and an angle of elevation of 26°. You need to find the height and length of the base of the ramp.
16Find leg lengths using an angle of elevation EXAMPLE 5Find leg lengths using an angle of elevationSOLUTIONSTEP 1Find the height.sin 26o=opp. hyp.Write ratio for sine of 26o.sin 26ox=14Substitute.14 sin 26o= xMultiply each side by 14.6.1xUse a calculator to simplify.ANSWERThe height is about 6.1 feet.
17Find leg lengths using an angle of elevation EXAMPLE 5Find leg lengths using an angle of elevationSTEP 2Find the length of the base.cos 26o=adj. hyp.Write ratio for cosine of 26o.cos 26oy=14Substitute.14 cos 26o= yMultiply each side by 14.12.6yUse a calculator to simplify.ANSWERThe length of the base is about 12.6 feet.
18EXAMPLE 6Use a special right triangle to find a sine and cosineUse a special right triangle to find the sine and cosine of a 60o angle.SOLUTIONUse the 30o - 60o - 90o Triangle Theorem to draw a right triangle with side lengths of 1, , and 2. Then set up sine and cosine ratios for the 60o angle.3sin 60o=opp. hyp.32cos 60o=adj. hyp.210.5000=
19GUIDED PRACTICEfor Examples 5 and 67.WHAT IF?In Example 5, suppose the angle of elevation is 35o. What is the new height and base length of the ramp?ANSWERabout 8 feet, about 11.5 ft8.Use a special right triangle to find the sine and cosine of a 30o angle.ANSWER12,3
20EXAMPLE 6Use a special right triangle to find a sine and cosineUse a special right triangle to find the sine and cosine of a 45 degree angle.
21Section 7.6Apply the Sine and Cosine RationsHomework: p1,2, 4-6, 8, 9, 11-13, 19-27p16-18,28, 29, 34-39