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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

6. The Law of Sines and Law of Cosines

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Exercise 3 Page 674

The Law of Sines relates the sine of each angle to the length of the opposite side.

69.8

Practice makes perfect

For any △ ABC, let the lengths of the sides opposite angles A, B, and C be a, b, and c, respectively.

The Law of Sines relates the sine of each angle to the length of the opposite side.

sin A/a=sin B/b=sin C/c We can find the third interior angle using the Triangle Angle Sum Theorem. 180- 55- 60= 65^(∘) Consider the given triangle with new information.

We know that the length of a side is 73 and that the measure of its opposite angle is 65. We want to find the length of the side that is opposite to the angle whose measure is 60. We can use the Law of Sines again! sin 65/73=sin 60/x Let's solve the above equation for x using the Cross Product Property.

sin 65/73=sin 60/x

▼

Solve for x

Cross multiply

sin 65* x=sin 60* 73

.LHS /sin 65.=.RHS /sin 65.

x=sin 60* 73/sin 65

Use a calculator

x=69.755391...

Round to 1 decimal place(s)

x≈ 69.8

Subchapter links

Exercises p.674-679