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Applications of Trig Functions EQ: How do I use trigonometry in real-life application problems? Angles of Elevation and Depression 4. A closed circuit television camera is mounted on a wall 7.4 feet above a security desk in an office building. It is used to view an entrance door 9.3 feet from the desk. Find the angle of depression from the camera lens to the entrance door. ? 7.4 feet ? 9.3 feet 5. The world’s longest escalator is the Leningrad Underground in Lenin Square. The escalator has an angle of elevation of 10.36° and a vertical rise of 195.8 ft. Find the length of the escalator. ? 195.8 feet 10.36° 6. Find the height of a flagpole which casts a shadow of 9.32 m when the sun makes and angle of 63 to the horizontal. 63 ? 63 9.32 m 7. A train must climb at a constant gradient of 5.5 m for every 200 m of track. Find the angle of incline. 5.5 m ? 8. Find , the pitch of the roof. Trigonometry and 3-D Figures EQ: How do you find trigonometric ratios to find unknown sides and angles in 3-D figures? 9. In the triangular prism, find DF and the angle AFD. 10. All edges of a square-based pyramid are 10 cm in length. Find the angle between the slant edge and a base diagonal. 11. Find the angle between QW and the base of the 3-D figure. 12. Find the angle PV makes with QV. 13. A symmetric square-based pyramid has base lengths of 6cm and height of 8cm as shown. Find the measure of the face TQR and the base Areas of Triangles EQ: How do you find the area of a triangle using trigonometry? Review What happens if you don’t know the height??? There are some cases where you don’t need the height to find the area… What happens if you don’t know the height??? There are some cases where you don’t need the height to find the area… You have two sides and the included angle Labeling a Triangle If you have a triangle ABC with angles A, B, C the sides opposite these angles are a, b, c Formula for the Area of a Triangle when you have 2 sides and the included angle. The area of triangle is half of the product of two sides and the sine of the included angle Find the area of the triangle: