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5.7 What If I Can’t Measure It? Pg. 21 Applying the Tangent Ratio

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5.7 – What If I Can’t Measure It? Applying The Tangent Ratio In this chapter you have learned how to find the legs of a right triangle using an angle. But how can you use this information? Today you and your team will use the tangent ratio to solve problems and answer questions.

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5.40 – STATUE OF LIBERTY Lindsay gets nose-bleeds whenever she is 300 feet above ground. During a class fieldtrip, her teacher asked if she wanted to climb to the top of the Statue of Liberty. Since she does not want to get a nose-bleed, she decided to take some measurements to figure out how high the torch of the statue is. She found a spot directly under the torch and then measured 42 feet away and determined that the angle up to the torch was 82°. Her eyes are 5ft above the ground. Should she climb to the top or will she get a nose-bleed? Draw a diagram that fits this situation. Justify your conclusion.

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82° 42ft 5ft x tan 82° = x. 42 x = ft No!

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5.41 – USING TANGENTS a. Find the height of each object in the picture. Show all work. x 90ft 6ft 48ft x 5.5ft

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1 +6ft

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1 +5.5ft

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b.What information was needed to find the height of the object? 1. ______________________________ 2. ______________________________ 3. ______________________________ height of eyes of person measuring Distance from object Angle of sight

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5.42 – HOW TALL IS IT? How tall is Mount Everest? How tall is the White House? Often we want to know a measurement of something we cannot easily measure with a ruler or tape measure. Today you will work with your team to measure the height of something on your school's campus in order to apply your new tangent tool. To do this, get a clinometer (a tool that measures a slope angle) and a tape measure from your teacher.

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a. Ensure everyone know what tasks they are in charge of.

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b. Complete the tasks listed above and find the length away from the object and the degree of the angle formed.

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???? 60in

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c. Complete the diagrams for the situations you measured while outside. Then use tangent ratios to find the height of the object. Is your answer reasonable? How accurate were you with the object you were able to measure?

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