Right Triangle Trigonometry: Finding Sides
Trigonometry is a branch of mathematics that studies relationships involving lengths and
angles of triangles.
Diagram:
X
Y
Z
Reference Angle: Angle we are focused on (NOT right angle)
____________
Opposite Side: Side OPPOSITE the reference angle ____________
Adjacent Side: Side between reference angle and right angle
Hypotenuse: Side across from right angle (longest side)
____________
____________
Trigonometric Ratios:
sin (reference) 
opp
hyp
cos (reference) 
adj
hyp
tan( reference) 
Ways to remember the trigonometric ratios:
(1)
(2)
SOH CAH TOA
Some Old Horse, Caught Another Horse, Taking Oats Away
opp
adj
1)
Which ratio represents sin x sin in the right triangle shown below?
a)
b)
c)
d)
2)
In the accompanying diagram of right triangle ABC,
.
What is
a)
b)
c)
d)
?
,
,
, and
In Problems 3-7 solve for x (round to the nearest tenths):
3)
6)
sin 40 
x
15
4)
A
12 feet
27
tan 15 
B
x
34
tan 22 
5)
25
x
7) D  90 , O  12
OG  36.5cm , OD  x
x
D
C
O
G
8)
In triangle ABC, C is a right angle, A  19 and CB  30 . Find the measure of
AC to the nearest hundredths.
9)
A ladder leans against a building making an angle of 43 degrees with the ground.
If the base of the ladder is 12 feet from the building, what is the length of the
ladder?
10)
A hot-air balloon is tied to the ground with two taut (straight) ropes, as shown in
the diagram below. One rope is directly under the balloon and makes a right
angle with the ground. The other rope forms an angle of 50º with the ground.
Determine the height, to the nearest foot, of the balloon directly above the ground.
Determine the distance, to the nearest foot, on the ground between the two ropes.
HOMEWORK
1)
Which equation shows a correct trigonometric ratio for angle A in the right
triangle below?
a)
b)
c)
d)
2)
What ratio represents
in the accompanying diagram of
?
3)
The figure below is of a trapezoid (a rectangle with an attached triangle).
E
A
B
D
C
If AE  22 , ED  14 and D  45 , find the area of rectangle ABCE.
4)
In the accompanying diagram of right triangle ABC,
and
.
Which single function could be used to find AB?
a)
b)
c)
d)
5)
In the accompanying diagram, x represents the length of a ladder that is leaning
against a wall of a building, and y represents the distance from the foot of the
ladder to the base of the wall. The ladder makes a 60° angle with the ground and
reaches a point on the wall 17 feet above the ground. Find the number of feet in x
and y.