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13-4: Tangent Ratio

13-4: Tangent Ratio. 13-4: Tangent Ratio. Trigonometry : the study of the properties of triangles Trigonometric Ratio : a ratio of the measures of two sides of a right triangle Tangent : Opposite Leg/ Adjacent Leg. 13-4: Tangent Ratio. Example: Find tan A and tan B tan A = /

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13-4: Tangent Ratio

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  1. 13-4: Tangent Ratio

  2. 13-4: Tangent Ratio • Trigonometry: the study of the properties of triangles • Trigonometric Ratio: a ratio of the measures of two sides of a right triangle • Tangent: Opposite Leg/Adjacent Leg

  3. 13-4: Tangent Ratio • Example: Find tan A and tan B • tan A = / • tan A = 9/40 • tan B = 40/9 • Your Turn: Find tan P and tan Q • tan P = ¾ • tan Q = 4/3 B opposite adjacent 41 9 A C 40

  4. 13-4: Tangent Ratio • The calculator has built-in values for the tangent ratios for all angles. • This means if you know the measure of an angle and one leg, you can find the measure of the other leg.

  5. 13-4: Tangent Ratio • Example • A surveyor standing at the edge of a canyon made the measurements below. Find the distance across the canyon fromD to F. • tan 70˚ = x/45 • 45  tan 70˚ = x(put in calculator) • 123.6365 m = x

  6. 13-4: Tangent Ratio • Angle of elevation: The angle formed by the line of sight and a horizontal line when looking up. • Angle of depression: The angle formed by the line of sight and a horizontal line when looking down. Angle of elevation Line of sight Angle of depression

  7. 13-4: Tangent Ratio • Example: A ranger whose eye level is 5 ft is standing 100 ft from a tree sights the top of the tree at a 40˚ angle of elevation. Find the height of the tree. • Draw a diagram (on board) • tan 40˚ = x/100 • 100  tan 40˚ = x • 83.9100 = x

  8. 13-4: Tangent Ratio • You can use the tan-1 function on your calculator to find the measure of an angle when you know the measures of the legs. • Example: Find the angle of elevation between the car and the helicopter • tan x = 95/40 • tan-1(95/40) = x • 67.2˚ = x

  9. 13-4: Tangent Ratio • Assignment • Worksheet 13-4

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