2.  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

3. 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 9 40 41 opposite adjacent

4.  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.  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

6.  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

7.  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.  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.  Assignment › Worksheet 13-4