7.6 Solving Right Triangle Problems.notebook 2015 05 26 May 26, 2015 7.6 Solving Problems with Right Triangles Application Problems involving right triangles require you to calculate the length or angle of a triangle. These problems can be set up with a right triangle and solved with the use of: • Pythagorean Theorem • Sum of Angles in a Triangle • Primary Trigonometric Trig. Ratios SOH CAH TOA Strategies: 1. Draw a sketch and label. 2. Create a mathematical model using the necessary equations or formulas. 3. Plan your solution ‐ what is the order of steps to solve your problem. Do you have to solve something else first before solving what is required? 4. Execute the plan. 5. Interpret your solutions. Are your answers reasonable? Do you have the correct unit of measurement? 1 7.6 Solving Right Triangle Problems.notebook May 26, 2015 Example 1: An airplane is approaching a runway at an angle of descent of 30o . What is the altitude of the airplane when it is 15 km along its flight path from the runway? angle of descent (or angle of depression) altitude angle of elevation 2 7.6 Solving Right Triangle Problems.notebook May 26, 2015 Example 2 A group of students are on an outdoor education trip. They leave their campsite and travel 240 m before reaching the first orienteering checkpoint. They turn, creating a 42° angle with their previous path, and travel another 180 m to get to the second checkpoint. They turn again and travel the shortest possible path back to their campsite. What area of the woods did their triangular route cover? campsite checkpoint # 1 checkpoint # 2 3 7.6 Solving Right Triangle Problems.notebook May 26, 2015 EXAMPLE 3 Ayesha is a forester. She uses a clinometer (a device used to measure angles of elevation) to sight the top of a tree. She measures an angle of 48°. She is standing 7.2 m from the tree, and her eyes are 1.6 m above ground. How tall is the tree? Homework: p.412‐414 #1, 4 ‐ 6, 10, 11, 14, 15 Reminder: Review tomorrow P.T. Thursday Test Friday 4