Transcript 8.5 Law of Sines and Cosines

8-5
8-5 Law
LawofofSines
Sinesand
andLaw
LawofofCosines
Cosines
HoltMcDougal
GeometryGeometry
Holt
8-5 Law of Sines and Law of Cosines
Warm Up
1. What is the third angle measure in a triangle with
angles measuring 65° and 43°?
Find each value. Round trigonometric
ratios to the nearest hundredth and angle
measures to the nearest degree.
2. sin 73°
3. cos 18°
4. tan 82°
5. sin-1 (0.34)
6. cos-1 (0.63)
7. tan-1 (2.75)
Holt McDougal Geometry
8-5 Law of Sines and Law of Cosines
Use your calculator to find each trigonometric
ratio. Round to the nearest hundredth.
A. tan 103°
B. cos 165°
C. sin 93°
Holt McDougal Geometry
8-5 Law of Sines and Law of Cosines
Use the law of sines in a non-right triangle in you are
provided with the measurements of an angle opposite
a side.
Holt McDougal Geometry
8-5 Law of Sines and Law of Cosines
Find the measure. Round lengths to the nearest
tenth and angle measures to the nearest degree.
FG
Holt McDougal Geometry
8-5 Law of Sines and Law of Cosines
Find the measure. Round lengths to the nearest
tenth and angle measures to the nearest
degree.
NP
Holt McDougal Geometry
8-5 Law of Sines and Law of Cosines
Find the measure. Round lengths to the nearest
tenth and angle measures to the nearest degree.
mQ
Holt McDougal Geometry
8-5 Law of Sines and Law of Cosines
Find the measure. Round lengths to the nearest
tenth and angle measures to the nearest degree.
mL
Holt McDougal Geometry
8-5 Law of Sines and Law of Cosines
Find the measure. Round lengths to the nearest
tenth and angle measures to the nearest
degree.
mX
Holt McDougal Geometry
8-5 Law of Sines and Law of Cosines
Find the measure. Round lengths to the nearest
tenth and angle measures to the nearest degree.
AC
Holt McDougal Geometry
8-5 Law of Sines and Law of Cosines
Solve each triangle.
f = 9.1, r = 20.1 , m⦟R = 107 ᵒ
Holt McDougal Geometry
8-5 Law of Sines and Law of Cosines
Solve each triangle.
m⦟R = 71ᵒ, m⦟F = 41 ᵒ, r = 7.4
Holt McDougal Geometry
8-5 Law of Sines and Law of Cosines
Solve each triangle.
m⦟R = 34 ᵒ , f = 9.1 , r = 27
Holt McDougal Geometry
8-5 Law of Sines and Law of Cosines
Solve each triangle.
m⦟F = 25 ᵒ , m⦟D = 52 ᵒ , r = 15.6
Holt McDougal Geometry
8-5 Law of Sines and Law of Cosines
Solve each triangle.
d = 30, r = 9.5 , m⦟D = 107 ᵒ
Holt McDougal Geometry
8-5 Law of Sines and Law of Cosines
Day 2
LAW OF COSINES
Holt McDougal Geometry
8-5 Law of Sines and Law of Cosines
Use the law of cosines if are NOT provided with a
side opposite an angle.
Holt McDougal Geometry
8-5 Law of Sines and Law of Cosines
Find the measure. Round lengths to the nearest
tenth and angle measures to the nearest degree.
XZ
Holt McDougal Geometry
8-5 Law of Sines and Law of Cosines
Find the measure. Round lengths to the nearest
tenth and angle measures to the nearest degree.
DE
Holt McDougal Geometry
8-5 Law of Sines and Law of Cosines
Find the measure. Round lengths to the nearest
tenth and angle measures to the nearest degree.
YZ
Holt McDougal Geometry
8-5 Law of Sines and Law of Cosines
Find the measure. Round lengths to the nearest
tenth and angle measures to the nearest degree.
mT
Holt McDougal Geometry
8-5 Law of Sines and Law of Cosines
Find the measure. Round lengths to the nearest
tenth and angle measures to the nearest
degree.
mK
Holt McDougal Geometry
8-5 Law of Sines and Law of Cosines
Find the measure. Round lengths to the nearest
tenth and angle measures to the nearest degree.
mR
Holt McDougal Geometry
8-5 Law of Sines and Law of Cosines
Solve the triangle. Round the length to the nearest tenth and the
angle measure to the nearest degree.
Holt McDougal Geometry
8-5 Law of Sines and Law of Cosines
What if…? Another engineer suggested using a cable attached
from the top of the tower to a point 31 m from the base. How
long would this cable be, and what angle would it make with the
ground? Round the length to the nearest tenth and the angle
measure to the nearest degree.
31 m
Holt McDougal Geometry
8-5 Law of Sines and Law of Cosines
Round lengths to the nearest tenth and
angle measures to the nearest degree.
1. mB = 20°, mC = 31° and b = 210. Find a.
2. a = 16, b = 10, and mC = 110°. Find c.
3. a = 20, b = 15, and c = 8.3. Find mA.
Holt McDougal Geometry
8-5 Law of Sines and Law of Cosines
4. An observer in tower A sees a fire 1554 ft away at an angle
of depression of 28°. To the nearest foot, how far is the fire
from an observer in tower B? To the nearest degree, what is
the angle of depression to the fire from tower B?
Holt McDougal Geometry