Pre Calculus Triangle Trigonometry
6.2 Right Triangle Trigonometry
Recall the right triangle ratio definitions of the trig functions: SOHCAHTOA
hyp
opp
adj
Ex 7: Find the values of all 6 trig functions for the angle shown.
3
2
θ
Ex 8: If
, find the values of the 5 other trigonometric functions.
1
Memorize these trig values for the following special angles:
θ,
in degrees
Ex. 9 : Find x.
0o
30o
45o
60o
Ex 10: Find x.
12
45o
x
90o
4
x
30o
Some Definitions:
Ex 11: A 20-ft ladder is leaning against a building. If the base of the ladder is 6 ft
from the base of the building, what is the angle of elevation of the ladder? How
high does the ladder reach on the building?
2
Ex. 12 A plane is flying within sight of the Gateway Arch in St. Louis, MO, at an
elevation of 35,000 feet. The pilot would like to estimate her distance from
the Gateway Arch. She finds the angle of depression to a point on the ground
below the arch is 22o.
(a) What is the distance between the plane and the arch?
(b) What is the distance between a point on the ground directly below
the plane and the arch?
Ex 13: A 600-ft guy wire is attached to the top of a communication tower.
If the wire makes an angle of 65o with the ground, how tall is the
communication tower?
3
Ex 14 A hot-air balloon is floating above a straight road. To estimate their
height above the ground, the balloonists simultaneously measure the angle
of depression to two consecutive mileposts on the road on the same side of
the balloon. The angles of depression are found to be 20o and 22o. How
high is the balloon?
4
tower
P. 507 #35
29.2o
5.6o
105
5
6