Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
10/22/2013 Right Triangle Trigonometric Ratios Note: Right triangle trig ratios are only of acute angles. Solving Right Triangles Notations: Sine of A: Cosine of A: Tangent of A: Cosecant of A: Secant of A: Cotangent of A: Trigonometry Radnor High School sin A cos A tan A csc A sec A cot A 2 BC AB AC cos A AB BC B tan A AC A Right Triangle Trigonometric Ratios opposite leg hypotenuse adjacent leg cos A hypotenuse opposite leg tan A adjacent leg sin A sin A c b hypotenuse opposite leg hypotenuse sec A adjacent leg adjacent leg cot A opposite leg csc A a C 1 sin A 1 sec A cos A 1 cot A tan A csc A SOHCAHTOA 3 Example 1: sinA 4 Example 2: Find the 6 trig ratios of A and B. Find the 6 trig ratios of A and B. A A 5 C 1 csc A 1 or cosA sec A 1 or tanA cot A or AB BC AB sec A AC AC cot A BC csc A 8 12 B C 5 8 B 6 1 10/22/2013 Example 3: Using inverse trig ratios on calculator Find the 6 trig ratios of A and B. If we know the value of a trig ratio of an acute angle, we can use the corresponding inverse trig ratio to find the measure of the angle. A 4 2 B C If sin A x then A sin 1 ( x) If cos A y then A cos 1 ( y ) If tan A z then A tan 1 ( z ) 7 8 Example 4: Solving Right Triangles Find the measure of angle A if a) sin A = 0.341 To solve a right triangle is to find all missing side lengths and missing angle measures from the given information. b) cos A = 0.742 c) tan A = 2.347 9 10 Example 5: Example 6: Solve the right triangle below. Solve the right triangle below. A A 7 12 C 15 B C 11 65 B 12 2 10/22/2013 Angles of Elevation or Depression An angle of elevation or depression is the angle formed by the line of sight and the horizontal line. of depression Looking up Lookingg down of elevation 13 Example 7: 14 Example 8: Tom knows when he stands 123 feet from the base of a flagpole, the angle of elevation to the top is 26. If his eyes are 5 feet 3 inches above the ground, find the height of the flagpole. The length of the shadow of a building 34.09 meters tall is 37.62 meters. Find the angle of elevation of the sun. 15 16 Example 9: An airplane is approaching an airport. The pilot knows that the plane’s altitude is 2000ft and the angle of depression from plane to the airport is 25. Help the pilot to find how far the plane is from the airport. 17 3