Free Printable Unit 3 Review - General Triangles

1.

State the number of possible triangles that can be formed using the given measurements.
$B=139\degree,\ a=12\ cm,\ b=35\ cm$

a)

Two Triangles

b)

One Triangle

c)

None

2.

State the number of possible triangles that can be formed using the given measurements.
$B=147\degree,\ a=25\ km,\ b=15\ km$

a)

Two Triangles

b)

One Triangle

c)

None

3.

State the number of possible triangles that can be formed using the given measurements.
$A=36\degree,\ c=30\ km,\ a=26\ km$

a)

Two Triangles

b)

One Triangle

c)

None

4.

What is the measure of angle A to the nearest degree?

a)

$58\degree$ and $122\degree$

b)

$78\degree$ and $12\degree$

c)

$78\degree$ and $102\degree$

d)

$78\degree$

5.

Find the indicated angle to the nearest degree.

a)

$49\degree$

b)

$29\degree$

c)

$49\degree$ and $131\degree$

d)

$29\degree$ and $151\degree$

6.

Solve the Triangle(s): $a=14$ , $b=6$ , $A=27\degree$

a)

no triangle possible

b)

B = 11.219^o, C = 141.781^o, c = 19.078

c)

B = 38.219^o, C = 114.781^o, c = 27.998

d)

B = 11.219^o, C = 141.781^o, c = 19.078

OR

B = 38.219^o, C = 114.781^o, c = 27.998

7.

Solve the Triangle(s): A = 26^o, a = 5, b = 9

a)

no triangle possible

b)

B = 14^o, C = 21^o, c = 8.7

c)

B = 52^o, C = 102^o, c = 11.2

d)

B = 52^o , C = 102^o, c = 11.2

OR

B = 128^o, C = 26^o, c = 5.0

8.

Solve the triangle
$C=103\degree,\ b=16cm,\ c=12cm$

a)

$A=67\degree,\ B=73\degree,\ a=5.7cm$ or $A=33\degree,\ B=107\degree,\ a=3.5cm$

b)

$A=65.4\degree,\ B=74.6\degree,\ a=5.7cm$ or $A=34.6\degree,\ B=105.4\degree,\ a=3.5cm$

c)

Not a triangle

d)

$A=65.4\degree,\ B=74.6\degree,\ a=7cm$ or $A=34.6\degree,\ B=105.4\degree,\ a=5cm$

9.

Solve the triangle
$A=141\degree,\ c=11m,\ a=17m$

a)

$C=24\degree,\ B=15\degree,\ b=8m$

b)

$C=24\degree,\ B=15\degree,\ b=7m$

c)

Not a triangle

d)

$C=30\degree,\ B=9\degree,\ b=7m$

10.

Solve the triangle
$B=31\degree,\ a=30cm,\ b=25cm$

a)

$A=110.8\degree,\ C=38.2\degree,\ c=45.4cm$ or $A=7.2\degree,\ C=141.8\degree,\ c=6.1cm$

b)

$C=110.8\degree,\ A=38.2\degree,\ c=47cm$ or $C=7.2\degree,\ A=141.8\degree,\ c=4cm$

c)

Not a triangle

d)

$C=110.8\degree,\ A=38.2\degree,\ c=45.4cm$ or $C=7.2\degree,\ A=141.8\degree,\ c=6.1cm$

11.

Find the obtuse solution of the triangle with $A=15\degree,\ a=5,\ b=10$

a)

$C=148.8\degree,\ B=16.2\degree,\ c=5.4$

b)

$B=148.8\degree,\ C=16.2\degree,\ c=13.9$

c)

$B=31.2\degree,\ C=133.8\degree,\ c=5.4$

d)

$B=148.8\degree,\ C=16.2\degree,\ c=5.4$

12.

Which scenario is the Ambiguous case concerned with?

a)

SSS

b)

SAS

c)

SSA

d)

AAS

13.

Given the triangle, find the area. Calculate to the nearest thousandth.

(a)

14.

Given the triangle, find the area. Calculate to the nearest thousandth.

(a)

15.

Find the area of triangle ABC.
A = $98\degree$ , b = 13mm, c = 8mm

a)

112.4 $mm^2$

b)

68.9 $mm^2$

c)

51.5 $mm^2$

d)

98.2 $mm^2$

16.

Find the area of $\Delta ABC$
if a = 9cm, b = 11cm, c = 16cm

a)

52.1 sq cm

b)

89.5 sq cm

c)

47.6 sq cm

d)

15.2 sq cm

17.

Find the area of $\Delta ABC$ if
a = 29in, b = 25in, c = 27 in

a)

312.2 sq in

b)

110.6 sq in

c)

19.5 sq in

d)

786.9 sq in

18.

Find the area of triangle ABC
A = $67\degree$ , b = 11yd, c = 24 yd

a)

209.1 $yd^2$

b)

58.2 $yd^2$

c)

112.8 $yd^2$

d)

121.5 $yd^2$

19.

Based on the given information determine the most efficient way for solving for the triangle's missing parts.

B= 70°, b=85, c=88

a)

Law of Sines

1 Triangle

b)

Ambiguous Case 0, 1, or 2 Triangles

c)

Law of Cosines

1 Triangle

20.

Based on the given information determine the most efficient way for solving for the triangle's missing parts.

A= 37°, a=8, b=14

a)

Law of Sines

1 Triangle

b)

Ambiguous Case

0, 1 or 2 Triangles

c)

Law of Cosines

1 Triangle

21.

Based on the given information determine the most efficient way for solving for the triangle's missing parts.

a = 8, c = 12, B = 57°

a)

Law of Sines

1 Triangle

b)

Ambiguos Case

0, 1, or 2 Triangles

c)

Law of Cosines

1 Triangle

22.

Based on the given information determine the most efficient way for solving for the triangle's missing parts.

V = 45°, v = 83, A = 79°

a)

Law of Sines

1 Triangle

b)

Ambiguous Case

0, 1, or 2 Triangles

c)

Law of Cosines

1 Triangle

23.

Based on the given information determine the number of unique triangles that may exist.
a = 255, b = 203, c = 172

a)

Law of Sines
1 Triangle

b)

Ambiguous Case
0, 1 or 2 Triangles

c)

Law of Cosines
1 Triangle

24.

Parker must find the distance from Point A to Point B on opposite sides of a lake. He locates Point C that is 860 feet from point A and 175 feet from Point B. He measures the angle at Point C to be 78 degrees. Find the distance from point A to point B.

a)

707643.5811

b)

841.2155

c)

707644.58

d)

841.2158

25.

In triangle ABC, a = 5, b = 6, c = 7. Which law would you need to use FIRST to solve the triangle?

a)

Law of Sines

b)

Law of Cosines

c)

Both trig laws

d)

None of these

26.

Find the length of PR by using Cosine Rule.

a)

$PR^2=9.2+8.5-\left(9.2\right)\left(8.5\right)\cos\ 89\degree$

b)

$PR^2=9.2^2+8.5^2-\left(9.2\right)^2\left(8.5\right)^2\cos\ 89\degree$

c)

$PR^2=9.2^2+8.5^2-2\left(9.2\right)\left(8.5\right)\cos\ 89\degree$

d)

$PR^2=9.2^2+8.5^2+2\left(9.2\right)\left(8.5\right)\cos\ 89\degree$

27.

What is the correct formula to find the area of ABC.

a)

$\frac{1}{2}\left(15+12\right)\sin\ 68\degree$

b)

$\frac{1}{2}\left(15+12\right)\cos\ 68\degree$

c)

$\frac{1}{2}\left(15\right)\left(12\right)\sin\ 68\degree$

d)

$\frac{1}{2}\left(15\right)\left(12\right)\cos\ 68\degree$

Unit 3 Review - General Triangles

Total questions: 27

Worksheet time: 41mins

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