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The Tangent Ratio Lesson 8-3 Geometry Additional Examples Write the tangent ratios for A and B. opposite BC 20 = = = tan A adjacent AC 21 opposite AC 21 = = = tan B adjacent BC 20 The Tangent Ratio Lesson 8-3 Geometry Additional Examples To measure the height of a tree, Alma walked 125 ft from the tree and measured a 32° angle from the ground to the top of the tree. Estimate the height of the tree. The tree forms a right angle with the ground, so you can use the tangent ratio to estimate the height of the tree. height tan 32° = 125 height = 125 (tan 32°) 125 32 78.108669 Use the tangent ratio. Solve for height. Use a calculator. The tree is about 78 ft tall. The Tangent Ratio Lesson 8-3 Geometry Additional Examples Find m R to the nearest degree. 47 tan R = 41 m R tan–1 47 41 So m R Find the tangent ratio. 47 41 48.900494 49. Use the inverse of the tangent. Use a calculator. Sine and Cosine Ratios Lesson 8-4 Geometry Additional Examples Use the triangle to find sin T, cos T, sin G, and cos G. Write your answer in simplest terms. 12 3 opposite = = sin T = hypotenuse 20 5 16 4 adjacent = = cos T = hypotenuse 20 5 16 4 opposite = = sin G = hypotenuse 20 5 12 3 adjacent = = cos G = hypotenuse 20 5 Sine and Cosine Ratios Lesson 8-4 Geometry Additional Examples A 20-ft. wire supporting a flagpole forms a 35˚ angle with the flagpole. To the nearest foot, how high is the flagpole? The flagpole, wire, and ground form a right triangle with the wire as the hypotenuse. Because you know an angle and the measures of its adjacent side and the hypotenuse, you can use the cosine ratio to find the height of the flagpole. height cos 35° = 20 height = 20 • cos 35° 20 35 16.383041 Use the cosine ratio. Solve for height. Use a calculator. The flagpole is about 16 ft tall. Sine and Cosine Ratios Lesson 8-4 Geometry Additional Examples A right triangle has a leg 1.5 units long and hypotenuse 4.0 units long. Find the measures of its acute angles to the nearest degree. Draw a diagram using the information given. Use the inverse of the cosine function to find m A. 1.5 cos A = 4.0 = 0.375 Use the cosine ratio. m A = cos–1(0.375) Use the inverse of the cosine. 0.375 67.975687 m A 68 Use a calculator. Round to the nearest degree. Sine and Cosine Ratios Lesson 8-4 Geometry Additional Examples (continued) To find m B, use the fact that the acute angles of a right triangle are complementary. m A + m B = 90 68 + m B 90 m B 22 Definition of complementary angles Substitute. The acute angles, rounded to the nearest degree, measure 68 and 22. Angles of Elevation and Depression Lesson 8-5 Geometry Additional Examples Describe 1 and 2 as they relate to the situation shown. One side of the angle of depression is a horizontal line. 1 is the angle of depression from the airplane to the building. One side of the angle of elevation is a horizontal line. 2 is the angle of elevation from the building to the airplane. Angles of Elevation and Depression Lesson 8-5 Geometry Additional Examples A surveyor stands 200 ft from a building to measure its height with a 5-ft tall theodolite. The angle of elevation to the top of the building is 35°. How tall is the building? Draw a diagram to represent the situation. x tan 35° = 200 Use the tangent ratio. x = 200 • tan 35° 200 35 140.041508 So x Solve for x. Use a calculator. 140. To find the height of the building, add the height of the Theodolite, which is 5 ft tall. The building is about 140 ft + 5 ft, or 145 ft tall. Angles of Elevation and Depression Lesson 8-5 Geometry Additional Examples An airplane flying 3500 ft above ground begins a 2° descent to land at an airport. How many miles from the airport is the airplane when it starts its descent? Draw a diagram to represent the situation. sin 2° = x= 3500 2 5280 100287.9792 18.993935 3500 x 3500 sin 2° Use the sine ratio. Solve for x. Use a calculator. Divide by 5280 to convert feet to miles. The airplane is about 19 mi from the airport when it starts its descent.