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8-3 Solving Right Triangles Holt Geometry 8-3 Solving Right Triangles In Short, To find a ratio or missing side length use Sin, Cos, Tan To find the angle use sin-1, Cos-1, Tan-1 Holt Geometry 8-3 Solving Right Triangles Example 2: Calculating Angle Measures from Trigonometric Ratios Use your calculator to find each angle measure to the nearest degree. A. cos-1(0.87) B. sin-1(0.85) C. tan-1(0.71) cos-1(0.87) 30° sin-1(0.85) 58° tan-1(0.71) 35° Holt Geometry 8-3 Solving Right Triangles Example 3: Solving Right Triangles Find the mR. Round angle measures to the nearest degree. Holt Geometry 8-3 Solving Right Triangles Example 4: Solving a Right Triangle in the Coordinate Plane The coordinates of the vertices of ∆PQR are P(–3, 3), Q(2, 3), and R(–3, –4). Find the side lengths to the nearest hundredth and the angle measures to the nearest degree. Holt Geometry 8-3 Solving Right Triangles Example 4 Continued Step 1 Find the side lengths. Plot points P, Q, and R. PR = 7 Y P By the Distance Formula, Q X R Holt Geometry PQ = 5 8-3 Solving Right Triangles Example 4 Continued Step 2 Find the angle measures. Y P mP = 90° Q X R The acute s of a rt. ∆ are comp. mR 90° – 54° 36° Holt Geometry 8-3 Solving Right Triangles An angle of elevation is the angle formed by a horizontal line and a line of sight to a point above the line. In the diagram, 1 is the angle of elevation from the tower T to the plane P. An angle of depression is the angle formed by a horizontal line and a line of sight to a point below the line. 2 is the angle of depression from the plane to the tower. Holt Geometry 8-3 Solving Right Triangles Example 1A: Classifying Angles of Elevation and Depression Classify each angle as an angle of elevation or an angle of depression. 1 It is an angle of depression. 4 It is an angle of elevation. Holt Geometry 8-3 Solving Right Triangles Use the diagram above to classify each angle as an angle of elevation or angle of depression. 1a. 5 It is an angle of depression. 1b. 6 It is an angle of elevation. Holt Geometry 8-3 Solving Right Triangles Check It Out! Example 2 What if…? Suppose the plane is at an altitude of 3500 ft and the angle of elevation from the airport to the plane is 29°. What is the horizontal distance between the plane and the airport? Round to the nearest foot. You are given the side opposite A, and x is the side adjacent to A. So write a tangent ratio. Multiply both sides by x and divide by tan 29°. x 6314 ft Simplify the expression. 29° Holt Geometry 3500 ft 8-3 Solving Right Triangles Check It Out! Example 3 What if…? Suppose the ranger sees another fire and the angle of depression to the fire is 3°. What is the horizontal distance to this fire? Round to the nearest foot. 3° By the Alternate Interior Angles Theorem, mF = 3°. Write a tangent ratio. x 1717 ft Holt Geometry Multiply both sides by x and divide by tan 3°. Simplify the expression.