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Develop an understanding of and apply special right triangle rules to find missing side lengths of right triangles, Practice Set C Name: Date: 1. Use your calculator to find the following values to four decimal places: tan 45˚ ________________ sin 45˚ ________________ cos 45˚ ________________ a. Fill in the chart below based on the figure above. Round decimal answers to the nearest ten thousandths. Follow the example in the first row of the chart. a 3 b c 3 tan ratio as sin ratio as cos ratio as ratio decimal ratio decimal ratio decimal 1 4 8 9 b. What do you notice? .7071 .7071 c. Why do you think the ratio for each trigonometric function stays the same even when the side length changes? 2. Use your calculator to find the following values to four decimal places: tan 30˚ ________________ sin 30˚ ________________ cos 30˚ ________________ tan 60˚ ________________ sin 60˚ ________________ cos 60˚ ________________ a. Fill in the chart below based on the figure above. Round decimal answers to the nearest ten thousandths. Follow the example in the first row of the chart. a b 3 c 6 8 9 10 b. What do you notice? tan ratio as sin ratio as cos ratio as ratio decimal ratio decimal ratio decimal .5774 .5 .8660 c. Why do you think the ratio for each trigonometric function stays the same even when the side length changes? d. Why do you think these two triangle types are called special? Might there be any other triangles that should be called special? Develop an understanding of and apply special right triangle rules to find missing side lengths of right triangles, Practice Set C Answer Key 1. Use your calculator to find the following values to four decimal places: tan 45˚ ____1___________ sin 45˚ ____.7071_______ cos 45˚ ____.7071________ a. Fill in the chart below based on the figure above. Round decimal answers to the nearest ten thousandths. Follow the example in the first row of the chart. a b 3 3 4 4 c tan ratio as sin ratio as cos ratio as ratio decimal ratio decimal ratio decimal 1 4sqrt 2 4/4 1 .7071 4/4sqrt .7071 2 5 5 5/5 1 5/5sqrt 4sqrt2 8 4sqrt2/ 1 4sqrt2 9sqrt2 9sqrt2/ /2 2 9 b. What do you notice? 9sqrt2/ 9sqrt2 4sqrt2/ .7071 sqrt2/2 .7071 5/5sqr .7071 t2 .7071 8 1 4/4sqr t2 2 4sqrt2 .7071 4sqrt2 .7071 /8 .7071 sqrt2/ 2 .7071 Answers may vary. The purpose of this question is for students to begin to see how the angle measure and the sides relate to each other. So student answers need to go beyond the same value appears. c. Why do you think the ratio for each trigonometric function stays the same even when the side length changes? Answers may vary. The purpose of this question is for students to begin to understand that all 45-45-90 triangles are similar. This idea is continued in the next lesson 2. Use your calculator to find the following values to four decimal places: tan 30˚ ____.5774_______ sin 30˚ _____.5__________ cos 30˚ ____.8660______ tan 60˚ ____1.7321______ sin 60˚ ______.8660______ cos 60˚ _____.5_________ a. Fill in the chart below based on the figure above. Round decimal answers to the nearest ten thousandths. Follow the example in the first row of the chart. a b 3 4 c tan ratio as sin ratio as cos ratio as ratio decimal ratio decimal ratio decimal 6 4sqrt3 8 .5774 4/4sqrt 3 .5774 .5 4/8 .5 .8660 4sqrt3 /8 .8660 5 10 5/5sqrt .5774 5/10 .5 3 3sqrt3 9 6sqrt3 3sqrt3/ 10 3/3 20sqrt sqrt3/3 .8660 /10 .5774 9 10sqrt 5sqrt3 3sqrt3/ .5 6sqrt3 .5774 3/3 sqrt3/2 sqrt3 9/6sqr .8660 t3 .5 10/20 .8660 sqrt3 b. What do you notice? Answers may vary. c. Why do you think the ratio for each trigonometric function stays the same even when the side length changes? Answers may vary. d. Why do you think these two triangle types are called special? Might there be any other triangles that should be called special? Answers may vary. The goal of this questions is to solidify the notion that these two types of right triangles have side lengths that create ratios with values that we can easily compute.