A flagpole is supported by three wires B A , B C and B D , as shown in this diagram. Find the area of triangle A B D .

Area of ∆ A B D = 1 2 · A D · B D · sin ( A D ^ B ) Consider ∆ A D B Applying cosine rule, cos ( A D ^ B ) = A D 2 + B D 2 - A B 2 2 A D · B D ⇒ cos ( A D ^ B ) = 12 2 + 20 2 - 28 2 2 ( 12 ) ( 20 ) = 144 + 400 - 784 480 ⇒ cos ( A D ^ B ) = - 240 480 = - 1 2 ⇒ A D ^ B = 120 ° ⇒ sin ( A D ^ B ) = 3 2 ∴ Area of ∆ A D B = 1 2 A D · B D sin ( A D ^ B ) = 1 2 20 12 3 2 = 60 3 m 2

A flagpole is supported by three wires B A , B C and B D , as shown in this diagram. Find the angle of elevation of the top of the tower from point C .

Angle of elevation of top of tower from C = B C ^ D Consider ∆ A D B Applying cosine rule, cos ( A D ^ B ) = A D 2 + B D 2 - A B 2 2 A D · B D ⇒ cos ( A D ^ B ) = 12 2 + 20 2 - 28 2 2 ( 12 ) ( 20 ) = 144 + 400 - 784 480 ⇒ cos ( A D ^ B ) = - 240 480 = - 1 2 ⇒ A D ^ B = 120 ° ⇒ B D ^ C = 180 ° - A D ^ B = 60 ° Consider, ∆ B C D From sine rule, sin C B D = sin D B C ⇒ sin C 12 = sin 60 ° 13 ⇒ sin C = 12 13 3 2 ⇒ sin C = 0 . 799 ≅ 0 . 8 ⇒ ∠ C = 53 · 1 ° Therefore, angle of elevation of top of tower from point C = 53 · 1 °

A flagpole is supported by three wires B A , B C and B D , as shown in this diagram. Show that the triangle A B C is not right angled.

Consider ∆ A D B Applying cosine rule, cos ( A D ^ B ) = A D 2 + B D 2 - A B 2 2 A D · B D ⇒ cos ( A D ^ B ) = 12 2 + 20 2 - 28 2 2 ( 12 ) ( 20 ) = 144 + 400 - 784 480 ⇒ cos ( A D ^ B ) = - 240 480 = - 1 2 ⇒ A D ^ B = 120 ° ⇒ B D ^ C = 180 ° - A D ^ B = 60 ° Consider, ∆ B C D From sine rule, sin C B D = sin D B C ⇒ sin C 12 = sin 60 ° 13 ⇒ sin C = 12 13 3 2 ⇒ sin C = 0 . 799 ≅ 0 . 8 ⇒ ∠ C = 53 · 1 ° Consider ∆ A B C Applying sine rule, sin A B C = sin C A B ⇒ sin A 13 = 0 . 8 28 ⇒ sin A = 0 . 371 ⇒ ∠ A = 21 . 7 ° From angle sum property ∠ A + ∠ B + ∠ C = 180 ° ⇒ ∠ B = 180 ° - 53 · 1 ° + 21 . 7 ° ⇒ ∠ B = 105 . 2 ° ∴ A B C is not a right angled triangle. Hence, shown.