Trigonometry Assignment

Running Head: Trigonometry Assignment 1
Trigonometry Assignment
Name
Institution Affiliation

TRIGONOMETRY ASSIGNMENT 2
Part A: Right-Angled and Non-Right Angled Trigonometry
Question 1: Sine rule
Part a)
The sine rule states that the ratio of the side of a triangle and the sine of the opposite angle to that
side is constant for all the three sides and the respective angles.
Considering the triangle ABC below, the sine rule is stated as
a
sin A = b
sin B = c
sin C
Where a , b , care the lengths of the sides and A , B , Care the angles opposite to each side
respectively (Flanders, 2014).
Part b)
The sine rule can be used when the length of one side of the triangle and its opposite angle is
known. If the length of one of the remaining sides or the magnitude of one of the remaining
angles is known, then all the angles and the sides of the triangle can be solved using the sine rule.
The rule cannot be used when all the sides are missing or all the angles are missing (Stewart &
Tall, 2015).
Part c)
Suppose a=6 cm ,∠ A=50°and∠ C=72°find the remaining sides of the triangle.
a
sin A = b
sin B = c
sin C
c= a × sinC
sin A = 6 ×sin 72
sin 50 =7.45 cm ( 2 d . p ) .
The angles in a triangle add up to 180 °
BA
C

TRIGONOMETRY ASSIGNMENT 3
∠ B=180 °− ( 72+50 )=58 °
b= a ×sin B
sin A =6 × sin 58
sin50 =6.64 cm
Part d)
Supposea=4 cm, b=6 cmand∠ B=54 ° ,find the remaining angles of the triangle.
a
sin A = b
sin B = c
sin C
sin A= a× sin B
b = 4 ×sin 54
6 =0.539
∠ A=sin−1 0.539=33.62°
The angles in a triangle add up to 180 °
∠ C=180° − ( 54+33.62 )=92.38°
Question 2: The cosine rule
Part a)
The cosine rule states that if sidesaand bare known and ∠ Cis the angle between the sides
(included angle), then sideccan be obtained by the following formula (Flanders, 2014)
c2=a2+ b2−2 ab cos C
Also, given aand c and∠ C, the sidec can be obtained by
b2=a2 +c2−2 ac cos B
Also, given band c and∠ A, the sidea can be obtained by
a2=b2 +c2−2 bc cos A
BA
C

TRIGONOMETRY ASSIGNMENT 4
Part b)
The cosine rule can be used when two sides and the include angle are known in a triangle. It is
also useful when all the sides of the triangle are known and all the angles are unknown.
The cosine rule cannot be used when only one or no side is known. Moreover, when two sides
are known and the given angle is not an included angle, then the cosine rule cannot be applied
(Stewart & Tall, 2015).
Part c)
Suppose a=5 cm ,b=6 cmand∠ C=72°find the remaining side c of the triangle.
c2=a2+ b2−2 ab cos C
c2=52+62−2 ×5 ×6 cos 72
c2=42.459
c=6.52cm
Part d)
Suppose a=5 cm ,b=6 cmandc=7 cmfind all the angles of the triangle.
c2=a2+ b2−2 ab cos C
Rearranging∠ C=cos−1
( a2+ b2−c2
2 ab )=cos−1
( 52 +62−72
2× 5 ×6 )=78.46°
b2=a2 +c2−2 ac cos B
Rearranging∠ B=cos−1
( a2 +c2−b2
2ac )=cos−1
(52+72−62
2 ×5 ×7 )=57.12°
a2=b2 +c2−2 bc cos A
Rearranging∠ A=cos−1
( b2 +c2−a2
2 bc )=cos−1
( 62 +72 −52
2 × 6× 7 )=44.42°