Solution for Trigonometry Problems in Calculus Assignment

This document presents a detailed solution to a calculus assignment involving trigonometry. The solution covers various problems, including those that require the application of the cosine and sine rules. It provides step-by-step solutions for calculating angles and sides of triangles, demonstrating the use of formulas and calculations to arrive at the correct answers. The problems involve finding unknown angles, sides, and determining if a triangle can be formed given certain parameters. The assignment covers a range of trigonometry concepts, including angle calculations, and solving for unknowns in different triangle configurations. The solution offers a clear and comprehensive guide to solving trigonometry problems, making it a valuable resource for students studying calculus.

Question 4
The following formula would be used.
Cos B= (a2+c2-b2)/2ac
Here, a= 26, b=x and c=35, B = 300
Hence, cos 300 = (262+352+x2)/2*26*35
Solving the above, x = 18.0
Question 5
The following formula would be used.
Cos C = (a2+b2-c2)/2ab
Here, C = 1200, a=22,b=10, c=x
Hence, cos 120 = (222 + 102 – x2)/(2*22*10)
Solving the above, x = 28.355
Hence, c= 28.355
The following formula would be used to compute the angle.
(a/sinA) = (c/sinC)
Here, a=22,c =28.355, C= 1200
Thus, (22/sinA) = (28.355/sin1200)
Solving the above A = 42.2 degrees
Also, angle B = (180-120-42.2)= 17.8 degrees
Question 6
Using the cosine rule, side c = 3.4
Using the sine rule, angle A =47.2 degrees and angle B =77.8 degrees
Question 7
Angle A = 34.1 degrees

Angle B = 105.3 degrees
Angle C = 40.6 degrees
Question 8
a1 = 81.3, a2 = 163,
Angle A1= 27.3, Angle A2 = 66.7,
Angle C1 = 109.7, Angle C2 = 70.3,
Question 9
C=DNE, angle B= DNE and angle C = DNE
No triangle is formed in this case.
Question 10
X = 2.13
Question 11
X=34.20
Question 12
Angle is 87.97
Question 13
X=23.7
Question 14
A=24

Question 15
A=42.4
Question 16
A =7.48
Question 17
28.69
Question 18
2.04