Step-by-step explanation:
the 3 main tools we need here :
- the sum of all angles in a triangle is always 180°.
- Pythagoras : c² = a² + b²
- the law is sine : a/sin(A) = b/sin(B) = c/sin(C)
b)
in order to be able to use the law of sine, we need to get the length of the baseline.
Pythagoras
baseline² = 8² + 5² = 64 + 25 = 89
baseline = sqrt(89)
8/sin(angle) = sqrt(89)/sin(90) = sqrt(89)/1 = sqrt(89)
sin(angle) = 8/ sqrt(89) = 0.847998304...
angle = 57.99461679...° ≈ 58° (or 57.99° officially rounded to the nearest hundredths)
c)
7/sin(x) = 12/sin(90) = 12/1 = 12
sin(x) = 7/12 = 0.583333333...
x = 35.68533471...° ≈ 35.69°
y = 180 - 90 - 35.69 = 54.31°
d)
9² = RG² + 7.5²
81 = RG² + 56.25
RG² = 24.75
RG = sqrt(24.75) = 4.974937186...
sqrt(24.75)/sin(T) = 9/sin(90) = 9/1 = 9
sin(T) = sqrt(24.75)/9 = 0.552770798...
T = 33.55730976...° ≈ 33.56°
