MAP4C - Geometry and Trigonometry: Lesson Assignment 3 Solutions

This document presents the solutions to MAP4C Lesson Assignment 3, which focuses on applying the Cosine Law to solve various triangle problems. The assignment includes questions that require students to determine unknown side lengths and angles using the Cosine Law formula. Students are expected to draw diagrams, write down the steps used to solve the problems, and identify the correct answers from multiple-choice options. The solutions demonstrate the application of the Cosine Law, involving calculations of side lengths, angles, and areas in different geometric scenarios. The assignment covers a range of problems from basic triangle calculations to more complex applications involving geometric shapes and real-world scenarios. The document provides detailed, step-by-step solutions to help students understand the concepts and solve similar problems.

MAP4C Lesson Assignment 3 Answers
Question 1
Length of a to the nearest whole number
Question 2
Cosine law (a2 = b2 + c2 – 2bc (cosA))
Cosine law a2= 92+182-2(9) cos26
a2=405-291.2044=113.7906
a=a= √113.7906
=10.667
=11
Choice “b”
Cosine law (a2 = b2 + c2 – 2bc (cosA))
b2=a2+c2-2ac (cosb)
b2=72+122-2(7×12) (cos100)
b =D
√222.1728
=14.905
≈15
Choice “b”
QUESTION 3
b2=a2+c2-2ac (cos b)
b2=242+172-(2×17×24) × (cos 58)
b2=432.5858
b=20.79
b=21
Choice”d”
A
C
B
A C
B
A
B 580 C
a
b
c

Question 4
cosA = a2−b2 −c2
−2bc
cosA =9.72=8.12 +6. 42
−(2 ×8.1 ×6.4) = −12.48
−103.68 =0.12037
A=co s−1 0.1237=83.0865
θ =830
Choice “a”
Question 5 Cos b = a2 −b2−¿ cc2
−2 bc ¿ - 2.42 −2.82 −3.92
−3 ×2.8 ×3.9 = −17.29
−21.84
cos−1A = 0.7916 = 37.658
=380
Question 6 Cos j = j2−h2−k2
−2 hk = 5.62−4.62−8.22
−2× 4.7 ×8.2
= −57.04
−77.08
Cos j = 0.74001
<J=cos−10.74001
=42.268
=420
Question 7
a2=b2 +c2−2 bc ¿-2×5.8×9.2× cos 68
a2=78.3019
a= 8.8488
a = 8.8km
Choice “b”
Choice “b”
Choice “b”
C B
A
9.7
6.48.1
θ b
2.4 2.8
3.9
C b
B b A b
θ b
H
K
J
θ b
4.7
5.6
8.2
A
C
B
6 80
5.8km
a
9.2km

Question 8
Cos A = a2 −b2 −c2
−2 bc
= 10.72−8.12−9.92
−2× 8.1× 9.9
Cos A = 0.30633
cos−10.30633
=72.16
=720
Choice “a”
Question 9
Finding a
a2=b2 +c2-2bc cos A
a2=7.62 +8.92- (2×8.9×7.6) cos 104
a2=169.693
a= 13.0267
≈13.0 km
fence Yard
Shed
460
580
7.6km 8.9km
aC
B
A
Choice “d”
θ b
A B
C
8.1 ft 10.7 ft
9.9 ft

Question 10
a2=b2 +c2 – 2bc cos A
a2 ¿ 322 +142-2×32×14cos 17
a2=√363.15
a = 19.0565
=19 km
Total distance = 19+32+14
= 65
1 lap = 65 km
? ==130 km
=2lapsChoice “b”
170
32 km
14km
19km
A(fire station)
C (police station)
B (school)