Chapter 9 Review
20 points
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Date____________Per_____
Trigonometric Ratios: SOH CAH TOA (do not forget about csc, sec, or cot)
Area = ½ bc sin A
Law of Sines:
𝑎
𝑏
=
sin 𝐴
sin 𝐵
or
=
Area = ½ ac sin B
𝑐
or
sin 𝐶
sin 𝐴
𝑎
or
=
Area = ½ ab sin C
sin 𝐵
𝑏
=
sin 𝐶
𝑐
Law of Cosines:
a2 = b2 + c2 – 2bc cos A
b2 = a2 + c2 – 2ac cos B
c2 = a2 + b2 – 2ab cos C
cos A = b2 + c2 – a2
2bc
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
cos B = a2 + c2 – b2
2ac
cos C = a2 + b2 – c2
2ab
Find the values of the six trigonometric functions for the angle θ if
a = 12, b = 5 and c = 13.
In triangle ABC, C = 90o, B = 35o and c = 12. Find a and b.
In triangle ABC, A = 90o, B = 64o and a = 27. Find b and c.
The legs of an isosceles triangle are 4 cm and the base angles are 45o.
Find the length of the base.
A mountain is approximately 15, 000 feet high. A trigonometry
student, several miles away, notes that the angle between level ground
and the top of the mountain is 40o. Estimate the distance to the base
of the mountain.
For an observer at point A, 250 m from the base of the building, the
angle of elevation to the top of the building is 5o. Find the height of
the building.
Find the area of the triangle ABC, if a = 3, b = 6 and C = 35o.
The area of the triangle ABC is 9. If a = 4 and b = 9, find all possible
measures of angle C.
Find the area of a parallelogram that has sides of 8 cm and 12 cm and
has acute angles of 80o. Try drawing a picture.
Find the area of a 5-sided regular polygon that is inscribed in a circle
of radius 4 cm. Try drawing a picture.
1
11-14. Approximate the remaining parts of the triangle described. Use may
use either the Law of Sines or Law of Cosines depending on which is most
appropriate. Use the figure below.
11.
12.
13.
14.
B = 38o, C = 65o, b = 13
a = 35, b = 52, c = 41
B = 105o, a = 2.6, c = 5.2
B = 28.5o, a = 10.2, b = 7.5
Heron’s formula is a alternative way to calculate the area of a triangle
and given by
Area = √s(s – a)(s – b)(s – c)
15.
16.
where s = a + b + c
2
If a = 3, b = 7 and c = 9, find the area of the triangle.
If a = 4, b = 5 and c = 7, find the area of the triangle.
17.
In order to determine the distance between two points, A and B, a
surveyor chooses a point C that is 365 yards from A and 520 yards
from B. If angle BAC has measure 44.5o, approximate the distance
between A and B. Use the law of sines. Draw a picture.
18.
A triangular plot of land has sides of length 425 feet, 360 feet, and
240 feet. Find the largest angle between any two sides.
In problems 19 – 20, approximate the area of triangle ABC. You should draw
pictures of the triangles.
19.
20.
a = 25, b = 21, c = 38
A = 32.5o, C = 95.7o, b = 15.3
2