 T RIGONOMETRY : the study of the properties of triangles  T RIGONOMETRIC R ATIO : a ratio of the measures of two sides of a right triangle  T ANGENT : Opposite Leg/Adjacent Leg

EExample: Find tan A and tan B ›t›tan A = / ›t›tan A = 9 / 40 ›t›tan B = 40 / 9 YYour Turn: Find tan P and tan Q ›t›tan P = ¾ ›t›tan Q = 4 / 3 B C A opposite adjacent

 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.

 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)  m = x

 A NGLE OF ELEVATION : The angle formed by the line of sight and a horizontal line when looking up.  A NGLE OF DEPRESSION : The angle formed by the line of sight and a horizontal line when looking down. Line of sight Angle of elevation Angle of depression

 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 › = x

 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

 Assignment › Worksheet 13-4