Holt McDougal Geometry

8-5 Law of Sines and Law of Cosines8-5 Law of Sines and Law of Cosines

Holt GeometryHolt McDougal Geometry

Holt McDougal Geometry

8-5 Law of Sines and Law of Cosines

Warm Up1. 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.

mQ

Holt McDougal Geometry

8-5 Law of Sines and Law of CosinesFind the measure. Round lengths to the nearest tenth and angle measures to the nearest degree.

mL

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.

mX

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 CosinesSolve each triangle.

f = 9.1, r = 20.1 , m R = 107⦟ ᵒ

Holt McDougal Geometry

8-5 Law of Sines and Law of CosinesSolve each triangle.

m⦟R = 71ᵒ, m F = 41⦟ ᵒ, r = 7.4

Holt McDougal Geometry

8-5 Law of Sines and Law of CosinesSolve 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

LAW OF COSINESDay 2

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 CosinesFind 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.

mT

Holt McDougal Geometry

8-5 Law of Sines and Law of CosinesFind the measure. Round lengths to the nearest tenth and angle measures to the nearest degree.mK

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.

mR

Holt McDougal Geometry

8-5 Law of Sines and Law of CosinesSolve 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 CosinesWhat 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. mB = 20°, mC = 31° and b = 210. Find a.

2. a = 16, b = 10, and mC = 110°. Find c.

3. a = 20, b = 15, and c = 8.3. Find mA.

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?