The Law of Cosines: Practice Level 2 | Geometry

Level 2 · Intermediate 0 / 12 answered

Question 1 of 12

1

A triangle has sides $26$ and $33$ meeting at $72^\circ$ . Find the third side to the nearest tenth.

Answer choices for question 1 A $47.9$ B $42.0$ C $35.1$ D $39.1$
2

Two rigid supports of lengths $45$ cm and $57$ cm meet at $127^\circ$ . How far apart are their free ends, to the nearest tenth of a centimeter?

Answer choices for question 2 A $91.4$ cm B $46.8$ cm C $72.6$ cm D $102.0$ cm
3

An angle lies between sides of lengths $17$ and $22$ . Its opposite side measures $31$ . Find the angle to the nearest tenth of a degree.

Answer choices for question 3 A $75.4^\circ$ B $104.6^\circ$ C $32.1^\circ$ D $43.4^\circ$
4

With $C$ at the origin, $CA$ follows the positive horizontal axis and $B$ is above it. The length of $CB$ is $18$ and $C=150^\circ$ . What is the exact horizontal coordinate of $B$ ?

Answer choices for question 4 A $9\sqrt3$ B $9$ C $-9$ D $-9\sqrt3$
5

The sides opposite $A$ , $B$ , and $C$ measure $15$ , $17$ , and $22$ in that order. Which is the closest measure of $A$ ?

Answer choices for question 5 A $50.5^\circ$ B $42.9^\circ$ C $86.6^\circ$ D $137.1^\circ$
6

The sides of a triangle measure $13$ , $20$ , and $24$ . Is the angle opposite the longest side acute, right, or obtuse?

Answer choices for question 6 A Acute B Right C Obtuse D The three sides do not form a triangle.
7

Sides of lengths $4$ and $11$ meet at $120^\circ$ . What is the exact third side length?

Answer choices for question 7 A $\sqrt{181}$ B $\sqrt{93}$ C $\sqrt{137}$ D $181$
8

A triangle has angle measures $54^\circ$ at $A$ and $81^\circ$ at $B$ . Side $AC$ has length $38$ m. Using the known opposite pair, find the length of $BC$ to the nearest tenth of a meter.

Answer choices for question 8 A $46.4$ m B $27.2$ m C $38.0$ m D $31.1$ m
9

Two triangles each have sides of lengths $g$ and $h$ . The included angles are supplementary and have cosine values $0.3$ and $-0.3$ . What is the larger opposite side square minus the smaller one?

Answer choices for question 9 A $1.2gh$ B $0.6gh$ C $0.9gh$ D $2gh$
10

The lengths of sides $a$ and $b$ of triangle $ABC$ are 17 and 23, respectively. The angle at $A$ is $32^\circ$ . Which first calculation is valid?

Answer choices for question 10 A $c^2=17^2+23^2-2(17)(23)\cos32^\circ$ B $\sin B=\dfrac{23\sin32^\circ}{17}$ C $B=180^\circ-32^\circ$ D $\sin B=\dfrac{17\sin32^\circ}{23}$
11

When three lengths are substituted into the cosine expression for an interior angle, the quotient is exactly $-1$ . What does this show about the proposed triangle?

Answer choices for question 11 A The angle would be $90^\circ$ , so the triangle is right. B The angle would be $0^\circ$ , so the two adjacent sides must be equal. C The angle would be $120^\circ$ , so the triangle is obtuse. D The angle would be $180^\circ$ , so the lengths give a straight arrangement.
12

Sides of lengths $29$ and $34$ meet at $46^\circ$ . Which proposed interval contains the third side?

Answer choices for question 12 A Greater than $5$ and less than $7$ B Greater than $43$ and less than $45$ C Greater than $24$ and less than $26$ D Greater than $57$ and less than $59$