Law of Cosines

Which of these triangles can you use the law of cosines to solve for a missing side?

B

Consider the proof. Given: In △ABC, BD ⊥ AC What is the missing reason in Step 8?

c. substitution

ΔDEF is an isosceles triangle with base angles E and F. What is the angle measure of the smallest angle in the triangle? Approximate to the nearest degree. ____ degrees What are the measures of the two congruent base angles? ____ degrees

14 83

A ferry transports passengers to three different ports. From port 1, the ferry travels east 3.5 miles to port 2. The ship then heads 15° east of south for 6 miles to reach port 3. What is the distance from port 3 to port 1? Draw a diagram to help you. Approximate to the nearest tenth of a mile. ______ miles

7.7 miles

On which triangle can the law of cosines be used to find the length of an unknown side?

B

Evelyn watches airplanes take off at an airport. She is 200 meters away from where the planes take off from the runway. The initial angle at takeoff of a plane is 12°. What is true when the plane is 100 meters away from takeoff? Check all that apply.

B, D, E

A parallelogram has side lengths of 13 and 17 and an angle that measures 64°.What is x, the length of the diagonal, to the nearest whole number?

a. 16

In ΔDEF, DE = 11, EF = 9, and angle E = 140°. Which equation correctly uses the law of cosines to solve for the third side?

a. e^2 = 11^2 + 9^2 − 2(11)(9)cos(140°)

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: How far must the outfielder throw the ball to return it to the pitcher? Round to the nearest foot.

b. 125 feet

Abby used the law of cosines for KMN to solve for k. k^2 = 31^2 + 53^2 - 2(31)(53)cos(37°) What additional information did Abby know that is not shown in the diagram?

a. mK = 37° and n = 31

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. By how many degrees did the direction of the boat change when it made its first turn? Round to the nearest degree.

b. 39 degrees

A pilot flies 720 miles from Dallas, Texas, to his first destination. After dropping off his cargo, he flies southeast 290 miles to his second destination. If the angle formed by his trip is 125°, what is the distance he will fly from the second destination back to Dallas?

b. 918 miles

Law of cosines: a^2 = b^2 + c^2 - 2bccos(A) What is the value of n to the nearest whole number?

b. 22

A surveyor measures the lengths of the sides of a triangular plot of land. What is the measure of the angle of the triangular plot at which the surveyor stands? Approximate to the nearest degree.

b. cos^-1(0.125) = 83°

Which equation correctly uses the law of cosines to solve for the missing side length of PQR?

b. p^2= 6^2 + 8^2 -2(6)(8)cos(39°)

The law of cosines is used to find the measure of Z.To the nearest whole degree, the measure of Z is

c. 51°

What is the measure of P to the nearest whole degree?

c. 57°