Free Practice Quiz Question List

07 Applications of Trigonometry Online Quiz Questions

Use this free practice quiz with 20 questions to review 07 Applications of Trigonometry, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

Which trigonometric ratio directly relates the opposite side and the adjacent side of a right triangle relative to an acute angle $\theta$ ?

A
$\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$
B
$\cos\theta=\frac{\text{opposite}}{\text{adjacent}}$
C
$\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$
D
$\tan\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$

True or false

1 point

True or false: An angle of depression from the top of an object is equal to the corresponding angle of elevation from the object below.

A
True
B
False

Choose one

1 point

A triangle is described by two side lengths and the angle included between them. Which method is most appropriate for finding the third side?

A
Law of Sines
B
Law of Cosines
C
Pythagorean theorem only
D
Heron's formula only

Choose all

1 point

Which information patterns can be solved using the Law of Sines? Select all that apply.

A
Two angles and the included side
B
Two angles and a non-included side
C
Three side lengths
D
Two sides and an angle opposite one of those sides

Fill in the blank

1 point

Complete both statements: The angles of any triangle sum to $^\circ$ . In a right triangle, the side opposite the right angle is the .

Written response

1 point

What is the standard name of the formula $K=\sqrt{s(s-a)(s-b)(s-c)}$ , used to find the area of a triangle from all three side lengths?

True or false

1 point

True or false: Reporting a triangle's area in linear units instead of square units is a common error.

A
True
B
False

Choose one

1 point

Two sides of a triangle have lengths $7$ and $10$ , and their included angle is $60^\circ$ . What is the approximate length of the third side?

A
$3$ units
B
$7.0$ units
C
Approximately $8.9$ units
D
$17$ units

Choose all

1 point

Which practices are part of a reliable trigonometric modeling process? Select all that apply.

A
Draw and label a diagram
B
Solve symbolically before rounding
C
Round intermediate values as early as possible
D
Check that the result has appropriate units

Fill in the blank

1 point

Complete both statements: If two sides $a$ and $b$ and the angle between them are known, the area is $K=$ . The angle used must be the .

Written response

1 point

A triangle has side lengths $a=8$ , $b=11$ , and $c=13$ . Find angle $C$ , opposite side $c$ , and round to the nearest tenth of a degree.

Open ended

1 point

Solve the triangle given $A=42^\circ$ , $B=68^\circ$ , and $a=10$ . Find $C$ , $b$ , and $c$ , rounding side lengths to the nearest tenth.

Choose one

1 point

A triangle has side lengths $13$ , $14$ , and $15$ . What is its area?

A
$42$ square units
B
$84$ square units
C
$126$ square units
D
$168$ square units

Choose one

1 point

Relative to an acute angle $\theta$ in a right triangle, which relationship should you use when the opposite side and hypotenuse are the relevant sides?

A
Sine
B
Cosine
C
Tangent
D
Pythagorean theorem

Choose one

1 point

A triangle problem gives two side lengths and an angle opposite one of those sides. Which approach is most appropriate?

A
Use the Pythagorean theorem; no ambiguity is possible.
B
Use the Law of Cosines; exactly one triangle is guaranteed.
C
Use the Law of Sines and check for the ambiguous case.
D
Use the base-height area formula before finding any angles.

Written response

1 point

What is the standard name of the formula used to find a triangle's area when all three side lengths are known?

Choose one

1 point

A right triangle has legs of length 9 units and 12 units. What is the length of its hypotenuse?

A
13
B
15
C
18
D
21

Choose one

1 point

What is the approximate area of a triangle with side lengths 8 units and 11 units enclosing an angle of $37^\circ$ ?

A
26.5 square units
B
44.0 square units
C
52.9 square units
D
88.0 square units

Written response

1 point

A triangle has side lengths 13, 14, and 15 units. What is its semiperimeter?

True or false

1 point

True or false: In a multistep trigonometric calculation, rounding an intermediate value before completing the calculation can change the final answer, so values should generally be rounded only at the end.

A
True
B
False