2. 1 Press Ctrl-A ©G Dear 2009 – Not to be sold/Free to use Elevation and Depression. Mathematics Stage 5.2

3. 2 Elevation & Depression (1/5) Elevation Depression θ θ Up Down

4. 3 Angle of Elevation (2/5) 100 m A boat is 100 m from a lighthouse. The height og the Lighthouse is 6 m. 100m θoθoθoθo What is the lighthouse’s angle of elevation? 6m tan θ o = 6 100 θ o = tan -1 (6 ÷ 100) θ o = 3.4336 o θ o = 3.4 o m

5. 4 Angle of Depression (3/5) An aero plane is 1 km from a runway. 1,000m What is the planes angle of depression? θOθOθOθO It is at a height of 300 m. 300 m Tan θ o = 300 1000 θ o = tan -1 (0.3) θ o = 16.6992442 o θ o = 17 o

6. 5 Angle of Elevation (4/5) 100m A boat is 100m from a lighthouse. angle of elevation30 o It has an angle of elevation of 30 o. 100m 30 o What is the height of the lighthouse? (h) h tan 30 o = h 100 h = 100 x Tan 30 o h = 57.735 026 919 h = 57.7 m

7. 6 Angle of Depression (5/5) An aero plane is 3 km from a runway. 3 km What is the altitude of the plane? 15 O The angle of depression is 15 o. a tan 15 o = a3a3 a = 3 x Tan 15 o a = 0.803 84 km a = 804 m