Hello, Fnus!

If you don't know the Law of Cosines, forget it!

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1) Using the cosine rule, show that: .AB .= .12√2(1 - cos75°)

It says: .AB² .= .12² + 12² - 2(12)(12)cos75°

. . . . . . .AB² .= .288 - 288·cos75° .= .288(1 - cos75°)

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Therefore: .AB .= .12√2(1 - cos75°)

Triangle OBP is a right triangle.2) Find the length of BP.

Angle POB = 37.5°.

. . . . . . . . . . . . . . . . . BP

We have: .tan37.5° .= .---- . → . BP .= .12·tan37.5°

. . . . . . . . . . . . . . . . . 12

Therefore: .BP .≈ .9.2