Chapter 8 1 Right Triangles Trigonometry In a

Chapter 8. 1 Right Triangles Trigonometry

In a right triangle, the shorter sides are called legs and the longest side (which is the one opposite the right angle) is called the hypotenuse c leg se b nu te po hy lega

Finding angle . adjacent c osit opp b h e a

Finding angle . osit e h a nt ac e opp ad j b c

Finding the angle from a ratio or decimal value. If sin 60° = or. 8660, then how do we get. 8660 to turn into 60°? ) = 22. 6° (. 8660) = 60° Find (. 6587) = 41. 2° Find (1) = 45° Find (- ) = Find (2. 87 ) = 70. 8° Find (. 7071) = 45° Find (2. 87 ) = Error! We use -53. 1°

Example: Solve the triangle. Find a, c, and *The sum of the triangle = 180 so, 40° = 180 -90 -40 = 50° adjacent Solve for a. Use 40° angle. opp Use tan. e osit b =2 c =50° a = 1. 68 Solve for c. Use ? ? Pythagorean Theorem a² + b² = c² 1. 68² + 2² = c² c = 2. 61

Example: Solve the triangle. Find c, , and Solve for c. a² + b² = c² 3² + 2² = c² adjacent c = 3. 61 opp e osit b =2 c Solve for . Use the given values. Use tan. a=3 *The sum of the triangle = 180 so, = 180 -90 -56. 3 = 33. 7° (3/2) = 56. 3°

b = 72. 79 meters or around 73 meters

Angle of Elevation and Angle of Depression

b = 251. 73 Now add the height of the transit 251. 73 + 2 = 253. 73 or about 254 meters.

A man climbs to the top of a mountain that is 1700 feet tall. He sees the cabin in the valley below at an angle of depression of 37°. How far away is the cabin from the base of the mountain? ? 37° tan 37° = 1700 x x ~ 2256 ft 1700 ft ?