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Solving for Triangle Sides with Algebra

32 questions

10th - 11th Grade

Mathematics

Solving for Triangle Sides with Algebra is a Grade 10–11 mathematics worksheet with 32 multiple-choice questions on solving for missing triangle sides and angles. Students classify triangles as acute, obtuse, or right using side lengths, apply the Pythagorean theorem to problems such as ladder measurements, and use SOH CAH TOA to calculate unknown sides and angles. The questions include both direct and inverse trigonometric-ratio problems, requiring students to identify relevant triangle relationships, select an appropriate operation, and interpret numerical answers with suitable rounding. This free printable worksheet supports independent practice, review, or formative assessment of algebraic and trigonometric problem solving. It includes a complete answer key for efficient checking and feedback.

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Worksheets

Solving for Triangle Sides with Algebra

Total questions: 32

Name
Class
Date
1.
Which set of sides would make a right triangle?
a)
4,5,6
b)
8,10,12
c)
5,12,13
d)
5,10,12
2.
A triangle has the following side lengths: 
AB = 12 units
BC = 10 units
AC = 16 units 
What type of triangle does this make?
a)
Acute
b)
Obtuse
c)
Right
d)
Equilateral 
3.
You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?
a)
25 feet
b)
26 feet
c)
27 feet
d)
28 feet
4.
A triangle has side lengths:
8, 8√3, 16  .  Is this triangle a right triangle, an acute triangle, or an obtuse triangle?
a)
right
b)
acute
c)
obtuse
5.
a)
x = 7, y = 7√2
b)
x = 14 y = 7√2
c)
x = 14√2 y = 7√2
d)
x = 14 y = 14√2
6.
a)
a = 5, b = 5
b)
a = 10, b = 10√2
c)
a = 10√2, b = 10√2
d)
a = 5√2, b = 5√2
7.
a)
v = 9√3, u = 6√3
b)
v = 6√3 u = 9√3
c)
v = 9, u = 6√3
d)
v = 3√6, u = 6√3
8.
a)
x = 3, y = 6
b)
x = 6√2, y = 12√2
c)
x = 2√3, y = 4√3
d)
x = 3√2, y = 6√2
9.
a)
20
b)
5.9
c)
33
d)
42
10.
a)
x=18
b)
x=18√3
c)
x=36√3
d)
x=12
11.
a)
y=11√2
b)
y=11
c)
y=22
d)
y=(11√2)/2
12.
a)
y=22.32 cm
b)
y=36.5 cm
c)
y=76.34 cm
d)
y=87.76 cm
13.
a)
x=24√3, y=24√2
b)
x=12√2, y=12√2
c)
x=24, y=24
d)
x=12, y=12
14.
a)
x=7, y=7√3
b)
x=7√2, y=7√2
c)
x=2, y=2
d)
x=7√3, y=7
15.
Use trig ratios (SOH CAH TOA) to solve for x 
a)
50.7
b)
50.1
c)
60.7
d)
61.0
16.
Use inverse trig ratios (SOH CAH TOA) to solve for the missing angle
a)
49°
b)
57°
c)
45°
d)
54°
17.
Use inverse trig ratios (SOH CAH TOA) to solve for the missing angle
a)
58°
b)
68°
c)
71°
d)
61°
18.
Find the missing side
a)
9
b)
26.9
c)
37
d)
18.2
19.
A triangle has side lengths:
20, 21, 28.  Is this triangle a right triangle, an acute triangle, or an obtuse triangle?
a)
right
b)
acute
c)
obtuse
20.
Solve for the missing angle
a)
50
b)
0.053
c)
36.9
d)
95
21.
Find the missing side lengths.
a)
A
b)
B
c)
C
d)
D
22.
Solve for x.
a)
24.20
b)
4.92
c)
290.4
d)
29.75
23.
Find the length of side w.
a)
21.4 cm
b)
18.0 cm
c)
36.5 cm
d)
43.6 cm
24.
What is the length of side x?
a)
6.57 cm
b)
7 cm
c)
7.44 cm
d)
26.33 cm
25.
What is the length of side w?
a)
38 cm
b)
30 cm
c)
50 cm
d)
76 cm
26.
What is the measure of angle A?
a)
50 degrees
b)
60 degrees
c)
78 degrees
d)
74 degrees
27.
Find the measure of angle R.
a)
2o
b)
67o
c)
74o
d)
92o
28.
1
a)
A
b)
B
c)
C
d)
D
29.
2
a)
A
b)
B
c)
C
d)
D
30.
What is the length of side x?
a)
130 cm
b)
112 cm
c)
150 cm
d)
105 cm
31.
Find angle A
a)
53.6
b)
13.3
c)
113.1
32.
Find BC
a)
17
b)
90
c)
18.99
Answer Key

Solving for Triangle Sides with Algebra

Total questions: 32

1.
c) 5,12,13
2.
b) Obtuse
3.
c) 27 feet
4.
a) right
5.
b) x = 14 y = 7√2
6.
d) a = 5√2, b = 5√2
7.
c) v = 9, u = 6√3
8.
d) x = 3√2, y = 6√2
9.
c) 33
10.
a) x=18
11.
b) y=11
12.
c) y=76.34 cm
13.
c) x=24, y=24
14.
d) x=7√3, y=7
15.
a) 50.7
16.
b) 57°
17.
c) 71°
18.
d) 18.2
19.
b) acute
20.
c) 36.9
21.
b) B
22.
d) 29.75
23.
b) 18.0 cm
24.
c) 7.44 cm
25.
b) 30 cm
26.
c) 78 degrees
27.
b) 67o
28.
b) B
29.
d) D
30.
d) 105 cm
31.
b) 13.3
32.
a) 17

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FAQs

What does this worksheet cover?

This worksheet covers solving for missing triangle sides and angles through 32 multiple-choice questions. Students classify triangles from their side lengths, use the Pythagorean theorem in numerical and ladder applications, and apply direct or inverse SOH CAH TOA ratios to find unknown measurements.

How can I use this worksheet to teach solving for triangle sides and angles?

Introduce the worksheet by reviewing how to identify the hypotenuse, opposite side, and adjacent side, then model when to use the Pythagorean theorem versus a trigonometric ratio. Have students explain why a set of side lengths represents an acute, obtuse, or right triangle before moving to the missing-side and inverse-trigonometry multiple-choice items.

What mistakes should I watch for when students complete this worksheet?

Watch for students using the wrong side as the hypotenuse, choosing SOH CAH TOA without identifying the known sides and angle, or using a direct ratio when an inverse ratio is needed to find an angle. Students may also classify triangles incorrectly by comparing side squares, forget to use degree mode, or select an answer before rounding their calculated measurement appropriately.

How do I assign and grade this worksheet?

This worksheet is available as a printable PDF and as a digital quiz on Wayground, with a complete answer key for the 32 multiple-choice questions. Printable submissions can be graded by scanning student work with the Wayground for Teachers app, while the digital quiz supports online response collection and grading.

How can I differentiate this triangle-solving worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or font size so the multiple-choice triangle problems and answer options are easier to navigate. You can also enable a dyslexia-friendly font or translate the worksheet into another language when those changes support access to the side-length, angle, and SOH CAH TOA questions.

Where can I find more worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to help students build essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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