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FPC
Math
10 Old Trigonometry Provincial Exam.
Name:____Key_____
1) Find the length of DB in centimetres. Answer to two decimal places.
Do you see 2 right triangles with the common side BD, let it be x.
The top right Δ has an angle of 43° with an opp side a, and
an adj side of x.
a
tan 43° =
, x · tan 43° = a
x
The bottom right Δ has an angle of 15° with an opp side b, and
an adj side of x.
tan 15° =
b
, x · tan 15° = b
x
,
________
________
Since a + b = 85 cm, so x · tan 43° + x · tan 15° = 85
x · ( tan 43° + tan 15°) = 85
x
=
85
= 70.81 cm
(tan 43  tan 15)
2) What is the exact value of the length of side x, in centimetres?
Do you see 2 right triangles with the
common side labeled as y.
Notice all the angles in the diagram
are special angles, ie: 30°, 60°.
Remember special angles have the
following properties.
Look at the blue right triangle:
5
5
5
cos 60° =
, y=
= 1
y
cos 60
2
1
cos 60° =
2
tan 60° =
3
=
1
3
y = 10 cm
Look at the red right triangle:
y
10
10
tan 60° =
, x=
=
cm
x
tan 60
3
FPC
Math
10 Old Trigonometry Provincial Exam.
Name:________________
1) Find the length of DB in centimetres. Answer to two decimal places.
2) What is the exact value of the length of side x, in centimetres?