Transcript Document

Lesson 42 - Review of Right Triangle
Trigonometry
Math 2 Honors – Santowski
Math 2 Honors - Santowski
1
(A) Review of Right Triangle Trig
Trigonometry is the study and solution of Triangles.
Solving a triangle means finding the value of each of
its sides and angles. The following terminology and
tactics will be important in the solving of triangles.
 Pythagorean Theorem (a2+b2=c2). Only for right
angle triangles
 Sine (sin), Cosecant (csc or 1/sin)
 Cosine (cos), Secant (sec or 1/cos)
 Tangent (tan), Cotangent (cot or 1/tan)
 Right/Oblique triangle
Math 2 Honors - Santowski
2
(A) Review of Right Triangle Trig

In a right triangle, the primary trigonometric ratios (which relate pairs of sides
in a ratio to a given reference angle) are as follows:

sine A = opposite side/hypotenuse side & the cosecant A = cscA = h/o
cosine A = adjacent side/hypotenuse side & the secant A = secA = h/a
tangent A = adjacent side/opposite side & the cotangent A = cotA = a/o



recall SOHCAHTOA as a way of remembering the trig. ratio and its
corresponding sides
Math 2 Honors - Santowski
3
(B) Examples – Right Triangle Trigonometry

Using the right triangle trig ratios, we can solve for
unknown sides and angles:

ex 1. Find a in ABC if b = 2.8, C = 90°, and A = 35°

ex 2. Find A in ABC if c = 4.5 and a = 3.5 and B = 90°

ex 3. Solve ABC if b = 4, a = 1.5 and B = 90°
Math 2 Honors - Santowski
4
Examples – Right Triangle Trigonometry

7/7/2015
Math SL1 - Santowski
5
Examples – Right Triangle Trigonometry

7/7/2015
Math SL1 - Santowski
6
(C) Cosine Law
B
c
a
C





b
A
The Cosine Law states the following:
a² = b² + c² - 2bccosA
b2 = a2 + c2 - 2accosB
c2 = a2 + b2 - 2abcosC
We can use the Cosine Law to work in right and non-right
triangles (oblique) in which we know all three sides (SSS) and
one in which we know two sides plus the contained angle (SAS).
Math 2 Honors - Santowski
7
(D) Law of Cosines:
A
b
Have: two sides,
included angle
Solve for: missing side
2
c
=
2
a
+
C
2
b
c
a
B
– 2 a b cos C
(missing side)2 = (one side)2 + (other side)2 – 2 (one side)(other side) cos(included angle)
Math 2 Honors - Santowski
8
(D) Law of Cosines:
A
Have: three sides
b
c
Solve for: missing angle
C
a
B
Side Opposite
Missing Angle
Missing Angle
a2 + b2 – c2
cos C =
2ab
Math 2 Honors - Santowski
9
(E) Cosine Law - Examples

Solve this triangle
B
c=5.2
a=2.4
A
b=3.5
Math 2 Honors - Santowski
C
10
(F) Examples Cosine Law

We can use these new trigonometric relationships in solving for
unknown sides and angles in acute triangles:

ex 1. Find c in CDE if C = 56°, d = 4.7 and e = 8.5

ex 2. Find G in GHJ if h = 5.9, g = 9.2 and j = 8.1

ex 3. Solve CDE if D = 49°, e = 3.7 and c = 5.1
Math 2 Honors - Santowski
11
(G) Review of the Sine Law

If we have a non right
triangle, we cannot use the
primary trig ratios, so we
must explore new
trigonometric relationships.

One such relationship is
called the Sine Law which
states the following:
a
b
c


sin A sin B sin C
7/7/2015
C

B
A
sin A sin B sin C
OR


a
b
c
Math 2 Honors - Santowski
12
(G) Law of Sines: Solve for Sides
Have: two angles, one
side opposite one of the
given angles
Solve for: missing side
opposite the other given
angle
A
b
c
C
a
B
Missing Side
a
b
=
sin A
sin B
7/7/2015
Math 2 Honors - Santowski
13
(G) Law of Sines: Solve for Angles
Have: two sides and one
of the opposite angles
Solve for: missing angle
opposite the other given
angle
Missing Angle
7/7/2015
A
b
c
C
a
B
a
b
=
sin A
sin B
Math 2 Honors - Santowski
14
(H) Examples Sine Law

We can use these new trigonometric relationships in
solving for unknown sides and angles in acute triangles:

ex 4. Find A in ABC if a = 10.4, c = 12.8 and C = 75°

ex 5. Find a in ABC if A = 84°, B = 36°, and b = 3.9

ex 6. Solve EFG if E = 82°, e = 11.8, and F = 25°

There is one limitation on the Sine Law, in that it can
only be applied if a side and its opposite angle is known.
If not, the Sine Law cannot be used.
7/7/2015
Math 2 Honors - Santowski
15
(H) Homework

Nelson S6.1
Math 2 Honors - Santowski
16