Step-by-step explanation:
2 things to remember :
1. the sum of all angles in a triangle is always 180°.
2. the law of sine
a/sin(A) = b/sin(B) = c/sin(C)
triangle 1 :
angle B = 180 - 62.2 - 43.8 = 74°.
a/sin(62.2) = 15.8/sin(74)
a = 15.8 × sin(62.2)/sin(74) = 14.53961961... in
c/sin(43.8) = 15.8/sin(74)
c = 15.8 × sin(43.8)/sin(74) = 11.37657122... in
triangle 2 :
14.9/sin(49) = 11.6/sin(A)
sin(A) = 11.6 × sin(49)/14.9 = 0.587559136...
angle A = 35.98398776...° ≈ 36°
angle C = 180 - 49 - 35.98398776... = 95.01601224...° ≈
≈ 95°
c/sin(95) = 14.9/sin(49)
c = 14.9 × sin(95)/sin(49) = 19.66708505...
newly weds triangle :
let's call the 2 sides a and b (25 m and 30 m).
the angle between them is 60°.
here we should use the extended Pythagoras for general triangles :
c² = a² + b² - 2×a×b×cos(C)
with c being the side opposite to the angle C.
so, we have in our case
c² = 25² + 30² - 2×25×30×cos(60) = 625 + 900 - 750 =
= 775
c = sqrt(775) = sqrt(25×31) = 5×sqrt(31) = 27.83882181... m
the area of the triangle we get via Heron's formula :
s = (a+b+c)/2 = (25+30+c)/2 = 41.41941091...
area = sqrt(s(s-a)(s-b)(s-c)) = sqrt(s(s-25)(s-30)(s-c)) =
= sqrt(105,468.75) = 324.7595264... m²
with Php 2000 per m² this would cost
324.7595264... × 2000 = Php 649,519.0528...
