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

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.

13 -4: Tangent Ratio � Example › A surveyor standing at the edge of a canyon made the measurements below. Find the distance across the canyon from D to F. �tan 70˚ = x/45 � 45 tan 70˚ = x (put in calculator) � 123. 6365 m = x

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 Angle of depression Line of sight

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 tan 40˚ = x 83. 9100 = x

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

13 -4: Tangent Ratio � Assignment › Worksheet 13 -4