Law of Cosines Answers

On which triangle can the law of cosines be used to find the length of an unknown side?Law of cosines: a2 = b2 + c2 – 2bccos(A)

A boat traveled north for 28 miles, then turned x° southwest and traveled for 25 miles before stopping. When it stopped, the boat was 18 miles from its starting point. Law of cosines:

On which triangle can the law of cosines be applied once to find an unknown angle measure?Law of cosines: a2 = b2 + c2 – 2bccos(A)

Law of cosines: a2 = b2 + c2 – 2bccos(A)

Law of cosines: a2 = b2 + c2 – 2bccos(A)

Law of cosines: a2 = b2 + c2 – 2bccos(A)

Consider the proof.Given: In △ABC, BD ⊥ ACProve: the formula for the law of cosines, a2 = b2 + c2 – 2bccos(A) Statement Reason1.In △ABC, BD ⊥ AC1.given2.In △ADB, c2 = x2 + h22.Pythagorean thm. 3.In △BDC, a2 = (b – x)2 + h23.Pythagorean thm. 4.a2 = b2 – 2bx + x2 + h24.prop. of multiplication5.a2 = b2 – 2bx + c25.substitution6.In △ADB, cos(A) = 6.def. cosine7.ccos(A) = x7.mult. prop. of equality8.a2 = b2 – 2bccos(A) + c28.?9.a2 = b2 + c2 – 2bccos(A)9.commutative propertyWhat is the missing reason in Step 8?

On a softball field, home plate is 43 feet from the pitcher’s mound. A ball is hit at an angle of 27° east of the pitcher’s mound. The ball travels 162 feet before it is caught by an outfielder. Law of cosines:

Law of cosines: a2 = b2 + c2 – 2bccos(A)

Law of cosines: a2 = b2 + c2 – 2bccos(A)