{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Pre-Calc Exam Notes 12

Pre-Calc Exam Notes 12 - 12 Chapter 1 Right Triangle...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
12 Chapter 1 Right Triangle Trigonometry §1.2 Example1.10 radicallow 3 30 A B C D E F radicalBig 3 2 radicalBig 3 2 2 1 45 Find the sine, cosine, and tangent of 75 . Solution: Since 75 = 45 + 30 , place a 30 60 90 right triangle ADB with legs of length radicallow 3 and 1 on top of the hypotenuse of a 45 45 90 right triangle ABC whose hypotenuse has length radicallow 3, as in the figure on the right. From Figure 1.2.2(a) we know that the length of each leg of ABC is the length of the hypotenuse divided by radicallow 2. So AC = BC = radicallow 3 radicallow 2 = radicalBig 3 2 . Draw DE perpendicular to AC , so that ADE is a right triangle. Since BAC = 45 and DAB = 30 , we see that DAE = 75 since it is the sum of those two angles. Thus, we need to find the sine, cosine, and tangent of DAE . Notice that ADE = 15 , since it is the complement of DAE . And ADB = 60 , since it is the complement of DAB . Draw BF perpendicular to DE , so that DFB is a right triangle.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}