Pre Calculus 11 Section 2.3 Sine Law

SECTION 2.3 SINE LAW

I) SINE LAW

The Sine Law is for solving triangles that are not R.T.

Name each side with the opposite angle

The Sine Law can only be used when you are givenone of the angles with its opposite side

There are 3 separate equations

EX: A TRIANGLE ABC HAS SIDE A = 12 CM, ANGLE A= 60°, AND ANGLE C = 45°. SOLVE FOR SIDE C.

PRACTICE: FIND THE VALUE OF “X”

Indicate the sides and angles

Formula

Cross Multiply and Solve for “X”

II) FINDING MISSING ANGLES

To find the angle, you need to use inverse sine

If the angle is obtuse, you need to find theangle in Quadrant #2

Ex: Find the value of “θ” to the nearest degreeEx: Find the value of “θ” to the nearest degree

Indicate the sides and angles

Formula

EXAMPLE 2: A TRIANGLE HAS SIDE A = 11 INCHES, ANGLEA = 40°, AND SIDE C = 8 INCHES. SOLVE FOR ANGLE C.

PRACTICE: FIND Θ TO THE NEAREST DEGREE

Formula

Angle “B” is an OBTUSE angle,

So it must be in Quadrant #2!!

Formula

Angle “B” is an OBTUSE angle,

So it must be in Quadrant #2!!

EX: THE ANGLE OF ELEVATION TO THE TOP OF THE TOWER IS 43°.IF YOU TRAVELS 100M CLOSER, THE ANGLE IS 75°. HOW TALL ISTHE TOWER? ASSUME THE PERSON IS ABOUT 1.5M TALL.

Make a Triangle and Gather Info

Find the Hypotenuse of the triangle

Use the Hypotenuse to find theopposite side

Height ofthe Tower

EXAMPLE 7: AT NOON, TWO TRACKING STATIONS ON EARTH ,STATION A IS 20 KM WEST OF STATION B, MEASURE A ROCKET THATWAS LAUNCHED FROM A WEATHER SATELLITE. FROM STATION ATHE ANGLE OF ELEVATION IS 41° AND FROM STATION B THE ANGLEOF ELEVATION WAS 75°. FIND THE HEIGHT OF THE ROCKET ABOVETHE EARTH.

PRACTICE: A SHIP LEAVES BATUMI ON A BEARING 300 ANDSAILS 860KM. THEY THEN CHANGE DIRECTION ON A BEARINGOF 222 AND SAIL FOR 580KM AND REACHED ISTANBUL. HOWFAR IS BATUMI FROM ISTANBUL?

Turkey

PROOF FOR THE SINE LAW

If we use another altitude forangle A, we can solve for the other part of the sine law

HW:

Assignment 2.3