Unit 6 · Test

Unit 6 test: Applications of Trigonometry

15 questions. Answer them all, then submit to see your score. Solutions unlock after you submit.

This test covers the law of sines, the law of cosines, triangle area, vector components and operations, magnitude and direction, and the dot product with angles, projections and work.

Question 1

In triangle $ABC$ , $A = 48^\circ$ , $C = 67^\circ$ and $c = 20$ . Find $a$ , to the nearest tenth.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 2

A triangle has $a = 11$ , $b = 15$ and $C = 38^\circ$ . Find $c$ , to the nearest tenth.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 3

A triangle has sides 8, 11 and 15. Find its largest angle, in degrees, to the nearest tenth.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 4

Two sides of a triangle are 12 cm and 9 cm, and the angle between them is $115^\circ$ . Find the area, to the nearest tenth of a square centimeter.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 5

How many triangles have $A = 30^\circ$ , $a = 5$ and $b = 8$ ?

Question 6

Find the area of a triangle with sides 13, 14 and 15.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 7

Find the component form of the vector from $P(-3, 4)$ to $Q(2, -8)$ . Enter it as $(a, b)$ .

Enter a point like (2, -3)

Question 8

Let $\mathbf{u} = \langle -1, 3 \rangle$ and $\mathbf{v} = \langle 4, -2 \rangle$ . Find $\|2\mathbf{u} - \mathbf{v}\|$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 9

A vector has magnitude 30 and direction angle $300^\circ$ . Find its components, rounded to the nearest hundredth. Enter them as $(a, b)$ .

Enter a point like (2, -3)

Question 10

Find the direction angle of $\langle -6, -2 \rangle$ , in degrees from $0^\circ$ to $360^\circ$ , to the nearest tenth.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 11

Find the angle between $\langle 3, -1 \rangle$ and $\langle 1, 5 \rangle$ , to the nearest tenth of a degree.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 12

Find $k$ so that $\langle k, 5 \rangle$ is orthogonal to $\langle -10, 4 \rangle$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 13

Find the vector projection of $\langle 5, -1 \rangle$ onto $\langle 2, 1 \rangle$ . Enter it as $(a, b)$ .

Enter a point like (2, -3)

Question 14

A force of 25 N, directed $20^\circ$ above the horizontal, pushes a cart 15 m along level ground. How much work is done, in joules, to the nearest tenth?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 15

For nonzero vectors $\mathbf{u}$ and $\mathbf{v}$ , $\mathbf{u} \cdot \mathbf{v} = -12$ . What can you conclude about the angle between them?