(a) If AB || DE, ∠AOD = 50° and ∠DPC = 160°, find the value of ∠DBE?

(b) A 15 m long ladder reached a window 12 m high from the ground when placed against a wall at a distance 'a'. Find the distance of the foot of the ladder from the wall.

[4 MARKS]

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Solution

(a) Steps: 1 Mark
Correct answer: 1 Mark
(b) Formula: 1 Mark
Result: 1 Mark

(a)

$∠ O A D = 50 ° (g i v e n) ∠ D O C = 180 ° - 50 ° = 130 ° (l i n e a r p a i r) ∠ D P C = 160 ° (g i v e n) ∠ D P O = 180 ° - 160 ° (L i n e a r p a i r) ∠ D P O = 20 ° I n △ D O P ∠ O D P = 180 ° - (130 ° + 20 °) (b y a n g l e s u m p r o p e r t y) ∠ O D P = 30 ° I n △ D B E ∠ D B E = 180 ° - (90 ° + 30 °) (B y a n g l e s u m p r o p e r t y) ∠ D B E = 60 °$

(b)

The wall and the ground are at right angle. Therefore the ladder, ground and the wall make the sides of a right-angled triangle.
$∴ a^{2} + 12^{2} = 15^{2}$
$\Rightarrow a^{2} = 225 - 144 = 81$
$a = \sqrt{8} 1 = 9 m$

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(a) If AB || DE, ∠AOD = 50° and ∠DPC = 160°, find the value of ∠DBE? (b) A 15 m long ladder reached a window 12 m high from the ground when placed against a wall at a distance 'a'. Find the distance of the foot of the ladder from the wall. [4 MARKS]

(a) If AB || DE, ∠AOD = 50° and ∠DPC = 160°, find the value of ∠DBE?

(b) A 15 m long ladder reached a window 12 m high from the ground when placed against a wall at a distance 'a'. Find the distance of the foot of the ladder from the wall.

[4 MARKS]