Download Solve for Sides in Right Triangles

Alternative Lessons – Mathematics – MFM2P
Student Resource
Using your Calculator - Sine, Cosine, and Tangent Ratios
Part A – Learning how to use your calculator for trigonometry.
1. Locate the sin, cos and tan buttons on your calculator.
2. Make sure that your calculator is on DEG (not GRAD or RAD). Usually it will say
so in small print in the display. If it is not in DEG, you need to get it into DEG mode.
Often this is done by ;pressing the DEG button until DEG shows in the display.
Some calculators require that you change this using a MODE button.
3. Determine your order of entry (see below). Once you know how your calculator
works for trig, you will use the same method every time.
Tan 45˚
Type 1
Press 45 then tan
Type 2
Press tan then 45
Answer should be 1
Sin 60˚
Type 1
Press 60 then sin
Answer should be 0.866
Type 2
Press sin then 60
Alternative Lessons – Mathematics – MFM2P
Student Resource
Part B – Solving for the sides of a right triangle
In order to solve for the sides of a right triangle you need 3 pieces of information: the right
angle, one other angle and one side. Find side BC, and then use Pythagorean theorem to find
side AC.
A
24
30˚
B
C
Steps:
1. Locate the required side and label it with a variable (letter). Use the small
letter of the angle opposite this side.
We will use ‘a’ to represent side BC
Also side AC will be represented by ‘b’
2. Using the given angle (not the right angle), label the three sides – hypotenuse,
opposite and adjacent.
Using angle 30˚…
AC or ‘b’ is the hypotenuse
24 is the opposite,
‘a’ is the adjacent
24
b
30˚
a
Alternative Lessons – Mathematics – MFM2P
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3. You should now have 2 of the 3 (hypotenuse, opposite and adjacent). Using
these two, create the appropriate trig ratio. Remember to use SOH CAH TOA
to help you.
We want ‘a’ which is the adjacent, and we have 24 which is the opposite.
The trig ratio that uses these two is TAN (TOA)
So that means that…
24
Tan 30˚=
a
4. Rearrange the equation so the unknown is on a side by itself.
Take the ‘a’ to the other side and multiply (do the opposite operation)
And now we get …
aTan30  24
Take the Tan 30˚ to the other side and divide (do the opposite operation)
Now we get….
24
a=
tan 30
5. Solve for the unknown using your calculator.
Now do this calculation on your calculator…
Type 1
Type 2
Press 24  30 tan 
Press 24  tan 30 
Your answer should be 41.56˚
6. Now the question also asks for the third side in the triangle. We can always
get the third side of a right triangle by using Pythagorean theorem.
Remember c 2  a 2  b 2
or
2
hypotenuse  side 2  otherside 2
So for this question…
b 2  242  41.62
b = 48.02
Alternative Lessons – Mathematics – MFM2P
Student Resource
We have almost solved this triangle completely, the only part missing is the third angle,
which we can get because the three angles add to 180˚
60˚
24
48
30˚
41.6
One more example…Find ‘EF’, and then solve for the remaining unknowns.
D
67˚
15
E
F
‘EF’ is represented by ‘d’ which is opposite to D.
15 is the hypotenuse.
f 2  152  13.82
Therefore
Sin 67˚=
d
15
Rearranging d = 15sin67˚
f = 5.87
Angle F = 180 – 90-67
Angle F = 23˚
d = 13.8
Done … actually it doesn’t take much time or space!
Alternative Lessons – Mathematics – MFM2P
Student Resource
Solving for Sides using Trig - Worksheet 1
1. Solve for the missing side using the sine ratio and then find the other side
using Pythagorean theorem.
a.
b.
8
x
c.
x
35
8
68
d.
28
d
75
23
13
p
Alternative Lessons – Mathematics – MFM2P
Student Resource
2. Solve for the missing side using the cosine ratio and then find the other side
using Pythagorean theorem.
a.
b.
48
w
5
17
60
r
c.
d.
g
s
59
32
13
17
Alternative Lessons – Mathematics – MFM2P
Student Resource
3. Solve for the missing side using the tangent ratio and then find the other
side using Pythagorean theorem.
a.
b.
75
k
h
15
21
19
c.
d.
52
13
65
m
c
12
Alternative Lessons – Mathematics – MFM2P
Student Resource
Solving for Sides using Trig – Worksheet 2
4. Solve for the missing side using the ratio of your choice and then solve for
the other missing pieces of information.
a.
18
g
23
b.
12
b
15
c.
y
25
57
d.
Alternative Lessons – Mathematics – MFM2P
Student Resource
h
37
9
e.
18
f
12
f.
k
45
4