Similar Triangles, Right Triangles, And The Definition Of The Sine, Cosine And Tangent Functions Of Angles Of A Right Triangle Worksheets With Answer Key Page 5

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Problems:
−
2
θ
θ
10. Given sin
=
and cot
is negative, what is the value of
9
θ
a) cos
(exactly)?
θ
θ
b) 6cos
- 2cot
(rounded to two decimal places)?
In Problems 11-15, use a calculator to approximate the answer to five decimal places.
5
φ
φ
φ
φ
− , find 6 sin
11. Given that angle
is a quadrant II angle and tan
=
+ 5 sec
.
8
9
θ
θ
θ
is a quadrant III angle and csc θ =
− . What is the value of tan
12. Angle
- 5 sec
?
5
θ
13. The point (0,-5) is on the terminal side of angle
in standard position.
θ
θ
What is the value of 2 tan
+ 5 csc
?
14. What is the value of 3 sin (864°) sec (164°) + 8 tan (-196°)?
π
π
20
+
−
15. What is the value of
2
sin
csc(
. 1
43
)
7
cos
?
11
7
16. Angles α and β are between 0° and 360° with cos α = -0.9063 and tan β = -0.4877.
Which of the following is a possible (approximate) value for α + β?
A) 51°
B) 129°
C) 309°
D) 361°
E) 669°
SOLVING RIGHT TRIANGLES
Given a right triangle and some data about it, we say we've "solved"
the triangle when we know the measures of its three sides and
three angles. In the special case of a right triangle ABC, with
C = 90° (see Figure T11), we are able to solve the triangle if we
know either 1) the measure of two sides, or 2) the measures of
Figure T11
one side and one additional angle.
Example: Given triangle ABC with C = 90° and a = 2.6, b = 5.1, solve the triangle.
Solution:
By the Pythagorean Theorem
=
+
=
2
2
2
c
(
. 2
) 6
5 (
) 1 .
32
.
77
.
=
=
Hence, the hypotenuse
c
32
.
77
. 5
72
(approximately)
Now we can calculate
2
6 .
=
=
sin
A
. 0
4542
32
.
77
so that A = 27°.
Figure T12
Then, B = 90° - 27° = 63°
NOTE: All calculator work is rounded, so results are necessarily approximate.
- 5 -

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