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Right Triangles
Introduction
Opposite
a
Sine = ------------------- example Sin A
= ------
Hypotenuse
c
Adjacent
b
Cosine = ------------------ example Cos A
= ------
Hypotenuse
c
Opposite
a
Tangent = ---------------- example Tan A
= ------
Adjacent
b
c2
= a2 + b2
and 180o
= A +
B + C
If you know one side of a right triangle and either A or B, you can solve
for the other two sides and the other angle. Pick the relationship with
only one unknown side. At this time there will only be one unknown term.
a = 5.32 cm and B
= 29.7o
a
a
5.32 cm
Tan B = ------ => b
= ------------ = --------------- = 9.33
cm
b
Tan B
Tan 29.7o
180o
= A +
B + C
=> A = 180o -
B -
C = 180o -
29.7o -
90.0o = 50.3o
c2
= a2 + b2
=> c = (a2
+ b2 ) 1/2
= ( (5.32 cm)2
+ (9.33
cm)2 ) 1/2 = 10.7 cm
If you know any two sides, you can find either Sine, Cosine, or Tangent.
a = 5.321 and
c = 8.549
Arcsine labeled Sin -1 on calculators is the angle with a
specific Sine. If the answer is to be given in degrees, set mode to Degree
instead of Radian.
a
5.321
A = Sin -1
(----) example A
= Sin -1 ( ------------ ) = 38.49o
if in radians A = 0.6718
c
8.549
Table of Contents
Right
Triangle Problems
All problems in this section refer to the above diagram.
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1. |
What is the value for B if a is 5.93 cm and c is
8.91 cm? |
|
2. |
What is the value for A if a is 23.6 cm and b is
16.2 cm? |
|
3. |
What is the value for c if B is 63.8° and a is
6.48 cm? |
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4. |
What is the value for B if a is 8.88 cm and b is
4.44 cm? |
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5. |
What is the value for a if A is 37.2° and b is
95.6 cm? |
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6. |
What is the value for b if A is 16.1° and c is
55.9 cm? |
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7. |
What is the value for A if a is 2.37 cm and c is
4.82 cm? |
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8. |
What is the value for a if A is 52.2° and b is
33.5 cm? |
Table of Contents
Right
Triangle Answers
All problems in this section refer to the above diagram.
|
| 1. |
What is the value for B if a is 5.93 cm and c is
8.91 cm?
|
|
a
a
5.93 cm
Cos B = --- => B = Cos -1 (
----) = Cos -1 (-------------) = 48.3o
c
c
8.91 cm |
a is the
adjacent side to B and c is the hypotenuse |
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|
|
| 2. |
What is the value for A if a is 23.6 cm and b is
16.2 cm?
|
|
a
a
23.6 cm
Tan A = --- => A = Tan -1 (
----) = Tan -1 (-------------) = 55.5o
b
b
16.2 cm |
a is the
opposite side to A and b is the adjacent side. |
|
|
|
| 3. |
What is the value for c if B is 63.8° and a is
6.48 cm?
|
|
a
a
6.48 cm
Cos B = --- => c = -----------
= --------------- = 14.7 cm
c
Cos B Cos 63.8o |
c is the
hypotenuse and a is the adjacent to B |
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|
|
| 4. |
What is the value for B if a is 8.88 cm and b is
4.44 cm?
|
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b
b
8.88 cm
Tan B = --- => B = Tan -1 (
----) = Tan -1 (-------------) = 63.4o
a
a
4.44 cm |
a is the
adjacent and b is the opposite of B. |
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|
|
| 5. |
What is the value for a if A is 37.2° and b is
95.6 cm?
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a
Tan A = --- => a = b Tan A = 95.6 cm x Tan 37.2o
= 72.6 cm
b |
b is the
adjacent and a is the opposite of A |
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|
|
| 6. |
What is the value for b if A is 16.1° and c is
55.9 cm?
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b
Cos A = --- => b = c Cos A = 55.9 cm x Cos 16.1o
= 53.7 cm
c |
b is the
adjacent and c is the hypotenuse to A. |
|
|
|
| 7. |
What is the value for A if a is 2.37 cm and c is
4.82 cm?
|
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a
a
2.37 cm
Sin A = --- => A = Sin -1
(----) = Sin -1 (-------------) = 29.5o
c
c
4.82 cm |
a is the
opposite and c is the hypotenuse to A. |
|
|
|
| 8. |
What is the value for a if A is 52.2° and b is
33.5 cm?
|
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a
Tan A = --- => a = b Tan A = 33.5 cm x Tan 52.2o
= 43.2 cm
b |
a is the
opposite and b is the adjacent to A. |
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Table of Contents | 
