Download 9.2 Using Trigonometry to Find Missing Sides of Right Triangles

9.4
Using Trigonometry to Find
Missing Sides of Right Triangles
Introduction:

What method can we use to find x in the
triangle below?
Pythagorean Theorem
•
Can we use the same method to find x in
the following triangle?

Trigonometry can help us to find
measures of sides and angles of right
triangles that we were unable to find
when our only tool was the Pythagorean
theorem.
Remember that we are using
Trigonometry at this point to find
missing sides of Right Triangles

What other angle (other than the right
angle) is given in the picture below?
Reference Angle
(starting angle)

Using the 34º angle as your
reference angle, would “x” be the
opposite leg, the adjacent leg, or the
hypotenuse? Label each side with a
O, A or H.
H
O
A
Remember the 3 Trig Ratios:
Sine (𝜃) =
𝑜𝑝𝑝
ℎ𝑦𝑝
Sine (𝜃) =
Cos (𝜃) =
𝑜𝑝𝑝
ℎ𝑦𝑝
“(𝜃)” Reference Angle
𝑎𝑑𝑗
𝐻𝑦𝑝
Tan (𝜃) =
𝑜𝑝𝑝
𝑎𝑑𝑗
Sine (𝜃) =

𝑜𝑝𝑝
ℎ𝑦𝑝
Remember that “(𝜃)” stands for the
reference angle. What is “(𝜃)” ?
 What is the length of the opposite leg?
 What is the length of the hypotenuse?
𝑥
12
Sine (34°) =
X = 12sin(34°) ≈12(0.5592) ≈ 6.71
So x ≈ 6.71
Let us look once again at the
following triangle:
• What is the measure of the other acute angle?
• Now repeat the same process that we followed in the previous slide.
• Use the new acute angle as the reference angle
𝑥
???? ( ? °) = 12
X = 12 ??? ( ? °) ≈12( ??) ≈ ????
So x ≈ ? ? ?
56°
Cos (56°) =
𝑥
12
X = 12cos(56°) ≈12(0.5592) ≈6.71
So x ≈ 6.71
Compare the value from the other angle of
34°. Notice that we obtain the same value
of “x” regardless of which reference angle
we choose to use.
You Try: Find x in the triangle. Round
answer to the nearest hundred
#1
18.4
x ≈ ___________
You Try: Find x in the triangle. Round
answer to the nearest hundred

#2
13.1
x ≈ ___________
You Try: Find x in the triangle. Round
answer to the nearest hundred
#3
7.5
x ≈ ___________
The End