Question

Find the lengths of the lettered angles and sides. No approximation for square root is allowed

Answer 1

• x = 30°, y = 45°
• w = 14√2, v = 7√2

Explanation:

ΔABC

• BC/AB = sin x
• 12/24 = sin x
• 1/2 = sin x
• x = 30°

ΔDBC

• DC = BC - given
• ∠C = 90° - given
• ΔDBC is isosceles right triangle

∠BDC ≅ ∠DBC ⇒ y = 45°

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ΔMPN is right isosceles triangle ⇒ MN = PN√2 = 14√2

• w = 14√2

ΔMKP is right isosceles triangle ⇒ MK = KP

• v = 1/2MN = 1/2(14√2) = 7√2