Help again! 三角學

1. The given information is "SSA" (means "Side, Side, Angle").
Since b is shorter than c, C can be an acute angle or obtuse angle, the SSA results in two triangles.

b=4, c=5, B=10°
By The Law of Sines,
sin(C)/c = sin(B)/b
sin(C)/5 = sin(10°)/4
sin(C) = [5×sin(10°)]/4
sin(C) = 0.2170...
C = sin^−1(0.2170...)
C = 12.5364...° or 167.4635…° [note: sin C=sin (180°-C)]
C = 12.5°or 167. 5° (to one decimal place)
A= 180°-B-C =180°-10°-12.5°=157.5° or
A= 180°-10°-167.5°=2.5°

By The Law of Sines,
sin(A)/a = sin(B)/b
sin(A)/a = sin(10°)/4
a= 4*sin(157.5°)/sin(10°)=8.82 (to 2 decimal places) or
a= 4*sin(2.5°)/sin(10°)=1.00 (to 2 decimal places)
The two triangles are: {a=8.82, b=4, c=5, A= 157.5°, B=10°, C = 12. 5°}, {a=1, b=4, c=5, A= 2.5°, B=10°, C = 167. 5°}

2. (a) The slope formed an angle of 90°-10°=80° with the tower, let this angle be A.
The first guy, the top and base of tower formed a “SAS” triangle.
A=80°, b=100, c=700
By the Law of Cosines,
a=√(b^2+c^2-2bc*cos A)
a=√(100^2+700^2-2(100)(700)*cos 80°)
a=689.70 (to 2 decimal places)

(b) The second guy, the middle and base of tower formed a right-angled triangle.
Let L be the length of wire which is the hypotenuse.
By the Pythagorus Theorem,
L=√[100^2+(700/2)^2]=364.01 (to 2 decimal places)