Level 2 · Intermediate ← Back to lesson

The Law of Sines: Practice

12 multiple-choice questions, progressively harder.

Level 2 · Intermediate 0 / 12 answered

Question 1 of 12

1

In triangle $ABC$ , $A$ measures $42^\circ$ , $a$ is 13 cm, and $B$ measures $59^\circ$ . Which expression gives $b$ in centimeters?

Answer choices for question 1 A $13\sin42^\circ/\sin59^\circ$ B $13\sin59^\circ/\sin42^\circ$ C $13/(\sin42^\circ\sin59^\circ)$ D $13\sin59^\circ/\sin79^\circ$
2

Angles $A$ and $C$ are $57^\circ$ and $68^\circ$ . Side $AC$ is 18 cm. Find $BC$ to the nearest tenth of a centimeter.

Answer choices for question 2 A $17.6$ cm B $19.9$ cm C $16.3$ cm D $18.4$ cm
3

In triangle $ABC$ , $A$ is $52^\circ$ , $B$ is $101^\circ$ , and $a$ is 17 m. Find $c$ to the nearest tenth of a meter.

Answer choices for question 3 A $9.8$ m B $7.7$ m C $19.9$ m D $13.7$ m
4

Stations $A$ and $B$ are 92 m apart and both sight target $C$ in their horizontal plane. The interior angle at $A$ is $47^\circ$ . At $B$ , the angle from the baseline extension pointing away from $A$ to the sight line is $125^\circ$ . Which expression gives $BC$ in meters?

Answer choices for question 4 A $92\sin55^\circ/\sin78^\circ$ B $92\sin47^\circ/\sin125^\circ$ C $92\sin47^\circ/\sin78^\circ$ D $92\sin78^\circ/\sin47^\circ$
5

Two triangles both have angles of $36^\circ$ at $A$ and $81^\circ$ at $B$ . The length of $AB$ in the second is twice its length in the first. How does the distance $AC$ change?

Answer choices for question 5 A It doubles. B It is unchanged. C It becomes four times as long. D It becomes half as long.
6

A triangle must satisfy $A=60^\circ$ , with $b$ of length 16 and $a$ of length 14. How many triangles fit?

Answer choices for question 6 A Zero, since $a<b$ B One, since the circle is tangent C Two D One, since the nearer crossing is behind $A$
7

Angle $A$ measures $120^\circ$ . The lengths of $a$ and $b$ are 7 and 8, respectively. The sine equation gives approximately $81.8^\circ$ and $98.2^\circ$ for $B$ . How many of these candidates are valid?

Answer choices for question 7 A Only the smaller candidate B Only the larger candidate C Both candidates D Zero
8

In an acute SSA setup, the radius $a$ equals the perpendicular distance from $C$ to ray $AB$ . The values of $a$ and $b$ are 4 and 11. What is $c$ exactly?

Answer choices for question 8 A $\sqrt{137}$ B $\sqrt{105}$ C $7$ D $15$
9

In an SSA problem $A$ is acute and $a>b$ . Why can the supplementary candidate for $B$ never give a second triangle?

Answer choices for question 9 A The perpendicular foot lies behind the ray start. B The circle is tangent to the ray. C The supplement has negative sine. D The ray start lies inside the circle, so only the far intersection is ahead of it.
10

In an SSA calculation, $A=74^\circ$ and the two candidates for $B$ are $85^\circ$ and $95^\circ$ . What is the smaller valid value of $C$ ?

Answer choices for question 10 A $11^\circ$ B $21^\circ$ C $16^\circ$ D $0^\circ$
11

The known angle $A$ is exactly $41.01^\circ$ . For one SSA candidate, $B$ is exactly $138.98^\circ$ . What does the angle-sum test say?

Answer choices for question 11 A Discard it because $C=0^\circ$ . B Keep the candidate because $C=0.01^\circ$ . C Discard it because $C=-0.01^\circ$ . D Keep it because $C=0.10^\circ$ .
12

Two distinct choices $B_1$ and $B_2$ on the ray give the same supplied side length $a$ . The foot of the perpendicular from $C$ to the ray is $H$ . How is $H$ positioned?

Answer choices for question 12 A It is between $A$ and $B_1$ , outside $B_1B_2$ . B It is farther along the ray than $B_2$ . C It is the midpoint of $B_1B_2$ . D It coincides with the nearer crossing.

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