1. 7.1 Right Triangle Trigonometry

2. A triangle in which one angle is a right angle is called a right triangle. The side opposite the right angle is called the hypotenuse, and the remaining two sides are called the legs of the triangle. c b a

3. y
P = (a, b) c b a x

4. Terminal side
Initial side

5. c b a

6. Function name Abbreviation Value
The six ratios of a right triangle are called trigonometric functions of acute angles and are defined as follows:
Function name
Abbreviation
Value

8. c = Hypotenuse = 13 b = Opposite = 12 13 12
Find the value of each of the six trigonometric functions of the angle
c = Hypotenuse = 13
b = Opposite = 12 13 12
Adjacent

10. Reciprocal Identities
Quotient Identities

11. c b a

12. c a b
To solve a right triangle means to find the missing lengths of its sides and the measurements of its angles.

13. c 4 b

14. h 25
h = 23.49

15. Yola just planted a Hybrid Elm
Yola just planted a Hybrid Elm. The nursery claims the tree grows 12 feet per year. Yola wants to verify the claim. She walks 100 feet from the base of the tree and, using a transit that is 2 feet off the ground, determines the angle of elevation is 5.7o. One year later, the angle of elevation 100 feet from the tree is 11.9o. Is the nursery’s claim true?

16. h = height of tree above transit g = growth of tree during first year
100 feet
2 feet
h = height of tree above transit
g = growth of tree during first year

17. Height of tree after 1 year: 2 + 9.98 + 11.09 = 23.07 feet