Question

3. [Maximum mark: 16]
An archaeological site is to be made accessible for viewing by the public. To do this,
archaeologists built two straight paths from point A to point B and from point B to point C as
shown in the following diagram. The length of path AB is 185 m, the length of path BC is 250 m,
and angle ABCˆ is 125
.

Answer 1

Given :-

• AB = 185 m .
• BC = 250 m .
• ∠ABC = 125° .

To Find :-

• AC = ?

Answer :-

we know that, according to cosine rule,

• cos θ = (a² + b² - c²)/2ab , where θ is angle between a and b .

from given data we have,

• a = 185 m .
• b = 250 m .
• c = AC = ?
• θ = 125° .

putting all values we get,

→ cos 125° = (185² + 250² - c²)/(2*185*250)

→ cos 125° * 2 * 185 * 250 = 34225 + 62500 - c²

→ cos 125° * 92500 = 34225 + 62500 - c²

→ (-0.574) * 92500 = 96725 - c²

→ (-53095) = 96725 - c²

→ c² = 96725 + 53095

→ c² = 149820

→ c = √(149820)

→ c ≈ 387 m (Ans.)

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