Answer:
Solved below
Explanation:
Q1) Hypotenuse² = a² + b²
Hypotenuse is side opposite to 90 degrees
Side AC is opposite to angle B
AC² = AB² + BC²
3.2² = 2.6² + BC²
BC = √3.48
BC = 1.87 cm
Q2 a) Use sin rule to calculate C
b/sin B = c/sin C
30/sin 60 = 25.2/sin C
sin C =21√3/50
Angle C = 46.7°
To find angle A
all 3 angles of a triangle are equal to 180°
A + B + C = 180°
A + 60 + 46.7 = 180°
Angle A = 73.3°
Use sin rule to find side BC
a/sin A = b/sin B
a/sin 73.3 = 30/sin 60
a = 33.2
Q2 b) Use sin rule to find angle E
f/sin F = e/sin E
62/sin 50 = 80/sin E
E = 81.3°
All 3 angles of a triangle are equal to 180 degrees.
D + E + F = 180°
D + 81.3 + 50 = 180°
Angle D = 48.7°
Use sin rule to calculate EF
f/sin F = d/sin D
62/ sin 50 = d/ sin 48.7
d = 60.8°
Q2 c) Use sin rule to find angle N
n/sin N = l/sin L
6.9/sin N = 3.4/sin 31
sin N = 6.9/3.4 * sin 31
N = sin inverse (1.045)
Math error!
Qb) Angle A can be found through the cosine rule
Angle A = cos inverse (a²+b²-c²/2ab)
Angle A = cos inverse (21.2²+11.6²-28.1²/2*21.2*11.6)
Angle A = 114.7°
Find angle B with sin rule
a/sin A = b/in B
21.2/sin 114.7 = 11.6/sin B
sin B = 21.2/sin 114.7 * 11.6
B = sin inverse (0.497)
B = 29.8°
All three angles of a triangle are equal to 180°
A+B+C = 180°
114.7+29.8+C=180°
C=35.5°
Q3) Find angle T through sine rule
t/sin T = r/sin R
4/sin T = 4.7/sin 57
T = 45.5°
All three angles of a triangle are equal to 180 degrees.
R + S + T = 180 degrees
57 + S + 45.4 = 180
S = 77.6°
RT can be found through sin rule
s/sin S = r/sin R
s/sin 77.6 = 4.7/sin 57
s = 5.5m
Q4) Angle A will be 33 degree.
BC will be 200 m
CD will be 384 m
AD can be found through the formula of sin
sin (angle) = opposite/hypotenuse
sin (33) = 384/AD
AD = 705.05 m
!!