The Law of Cosines: Practice Level 1 | Geometry

Level 1 · Foundational 0 / 12 answered

Question 1 of 12

1

In triangle $KLM$ , sides $KL$ and $KM$ have lengths $22$ and $28$ . Which angle appears in the cosine term of the equation for $LM^2$ ?

Answer choices for question 1 A $L$ B $K$ C $M$ D The larger of $L$ and $M$
2

The lengths opposite $A$ , $B$ , and $C$ are $a$ , $b$ , and $c$ . Which equation isolates the square of the side opposite $B$ ?

Answer choices for question 2 A $b^2=a^2+c^2-2ab\cos B$ B $b^2=a^2+c^2-2ac\cos C$ C $b^2=a^2+c^2+2ac\cos B$ D $b^2=a^2+c^2-2ac\cos B$
3

Place $C$ at the origin, with $A$ to its right and $B$ above the horizontal axis. The angle at $C$ is obtuse. Where is the perpendicular foot from $B$ on the horizontal line?

Answer choices for question 3 A To the left of $C$ B Between $C$ and $A$ C At $C$ D To the right of $A$
4

Two sides of lengths $r$ and $s$ meet at a right angle. What is the square of the distance between their other endpoints?

Answer choices for question 4 A $(r+s)^2$ B $r^2+s^2$ C $r^2-s^2$ D $2rs$
5

The known parts of triangle $ABC$ are sides $AB$ and $AC$ and angle $A$ . What type of data is this?

Answer choices for question 5 A SSS B SSA C SAS D ASA
6

The lengths of sides $a$ , $b$ , and $c$ of a triangle are 20, 21, and 29, respectively. Which angle is opposite the longest side?

Answer choices for question 6 A $A$ B $B$ C The data do not identify the angle. D $C$
7

The included angle between sides of lengths $u$ and $v$ is acute. How does the square of the third side compare with $u^2+v^2$ ?

Answer choices for question 7 A It is larger. B It is equal. C It is smaller. D Its comparison depends on which of $u$ and $v$ is longer.
8

In a triangle, $C$ is opposite $c$ . With all three side lengths known, which expression gives the cosine of $C$ ?

Answer choices for question 8 A $\dfrac{a^2+b^2-c^2}{2ab}$ B $\dfrac{c^2-a^2-b^2}{2ab}$ C $\dfrac{a^2+c^2-b^2}{2ac}$ D $\dfrac{a^2+b^2-c^2}{2bc}$
9

An interior angle has cosine $-0.24$ . Which operation gives its measure in degree mode?

Answer choices for question 9 A Apply cosine to $-0.24$ degrees. B Take the reciprocal of $-0.24$ . C Apply inverse sine to $0.24$ . D Apply inverse cosine to $-0.24$ .
10

Which set of lengths can form a nondegenerate triangle?

Answer choices for question 10 A $9$ , $15$ , $24$ B $10$ , $13$ , $24$ C $11$ , $14$ , $24$ D $8$ , $12$ , $21$
11

Two sides and their included angle are known. Which method can find the opposite side directly?

Answer choices for question 11 A Use the Law of Cosines and take the positive square root. B Use the Law of Sines with a known opposite pair. C Use inverse cosine on a ratio of the two known sides. D Use the angle sum to find the opposite side.
12

A surveyor knows side $AB$ and the angles at $A$ and $B$ . What is a valid first route to the length of $AC$ ?

Answer choices for question 12 A Treat $A$ and $B$ as the two lengths in the cosine law. B Find angle $C$ by the angle sum, then use the sine law. C Use $A$ as the angle opposite $AB$ . D Use the cosine law with the one known length and two known angles.