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## 1.5 Solving Right Triangles

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**1.5Solving Right Triangles**JMerrill, 2005 Revised 2009**Recall from Last Week**SOH-CAH-TOA • Sine: abbreviation: sin = • Cosine: abbreviation: cos = • Tangent: abbreviation: tan = • These are the ratios of 2 sides.**Evaluating with a Calculator When**• Mode is in degrees (for now!) • Solve: • cos 41o = tan 87o = • sin 18o = cos 180o = • These are still the ratios of 2 sides—in decimal form.**A plane is one mile above sea level when it begins to climb**at a constant angle of 2 for the next 70 ground miles. How far above sea level is the plane after its climb? So, about 3 ½ miles total. Application—Finding the Length of a Side 2o x 70**You do:**• A 16-foot ladder is propped against a building. The angle it forms with the ground measures 55. How far up the side of the building does the ladder reach? 16 x 55o**To find the measure of an angle you must take the inverse of**the function. The inverse tangent, for example, is written tan-1. On your calculator, you push 2nd tan.Anytime you are looking for the angle, you push the 2nd button! θ is the Greek symbol for theta (lower case). It will be used to represent an angle in degrees. 553 100 Finding an Angle θ**Angle of Elevation**• Angle of elevation is the angle formed by the horizontal line of sight to an object that is above the horizontal line.**Angle of Depression**• Angle of depression is the angle formed by the horizontal line of sight to an object that is below the horizontal line.**How far are you from the ground?**How tall is the pole? Solutions You are approximately 20.1 feet from the ground. From your position to the top of the pole is approximately 34.97 feet. Therefore, 20.1 + 34.97 = 55.07. Thus, the pole is about 55.07 feet tall.**Navigation**• Direction is often given as a measure of an acute angle with respect to the north-south vertical line. A bearing (or heading) of N 20o E means that the plane/ship is bearing 20o to the east of north. • So, S 48o W means? • 48o to the west of south**Example**• A jet takes off on a bearing of N 28o E, flies 5 miles, then makes a left (90o) turn and flies 12 miles. If the control tower operator wanted to locate the plane, what bearing would she use?