Right Triangles Trigonometry Chapter 8.1 Right Triangles Trigonometry

 hypotenuse c b leg  leg a 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  hypotenuse c b leg  leg a

Finding angle .  adjacent h opposite b c  a

Finding angle .  b c opposite h  adjacent a

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° Find ( ) = We use (.8660) = 60° Find (1) = 45° Find (.6587) = 41.2° Find (- ) = -53.1° Find (2.87 ) = 70.8° Find (.7071) = 45° Find (2.87 ) = Error!

Example: Solve the triangle. Find a, c, and  *The sum of the triangle = 180 so,  = 180-90-40 = 50° 40° adjacent c Solve for a. Use 40° angle. b =2 Use tan. opposite  =50° a = 1.68 a = 1.68 Solve for c. Use ???? Pythagorean Theorem a² + b² = c² 1.68² + 2² = c² c = 2.61 c = 2.61

Example: Solve the triangle. Find c, ,and  Solve for c.  a² + b² = c² 3² + 2² = c² c = 3.61 adjacent c b =2 opposite 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

= 12.7°

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 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° 1700 tan 37° = x x ~ 2256 ft 1700ft ?