The height of the balloon above the ground is 554 ft.
- I have attached a diagram where i have divided the triangle shown into 2.
From the attached image, the third angle in triangle 1 would be;
180 - (90 + 85) = 5°
The supplementary angle in triangle 2 to 85° in triangle 1 is;
180 - 85 = 95°(because supplementary angles add up to 180)
The third angle of triangle 2 is; 180 - (95 + 75) = 10°
- If we label the shared slant side between the two triangles as z, the we can use sine rule to find z from triangle 2;
100/sin10 = z/sin 75
z = 100(sin 75)/(sin 10)
- Applying trigonometric ratio to triangle 1, we can find h as;
h/z = sin 85
h = z sin 85
h = [100(sin 75)/(sin 10)] × sin 85
h ≈ 554 ft
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