Question

PLEASE ANSWER QUICK I NEED IT!!!!
ABCD is a rectangular hoarding and PQ, BP and BQ are three piece of wood nailed at back to support hoarding

Given that BP = 5.7 and BQ = 4.8 and
1. width of hoarding BC

2. Length of AP

3. the area enclosed by three pieces of wood, (triangle)PBQ

Answer 1

Solution :-

Since ABCD is a rectangle, each angle is equal to 90° .

So,

→ ∠BCD = 90°

then, in right angled ∆BCQ we have,

→ cos 52° = BC/BQ

→ cos 52° = BC/4.8

→ BC = cos 52° * 4.8

→ BC = 0.616 * 4.8

→ BC ≈ 2.96 cm (Ans.)

Again,

→ ∠ABC = 90°

then,

→ ∠PBA = 90° - (26° + 52°) = 90° - 78° = 12°

Now, in right angled ∆PAB we have,

→ sin ∠PBA = AP/PB

→ sin 12° = AP/5.7

→ AP = sin 12° * 5.7

→ AP = 0.207 * 5.7

→ AP ≈ 1.19 cm (Ans.)

also,

→ Area (∆PBQ) = (1/2) * QB * BP * sin ∠QBP

→ Area (∆PBQ) = (1/2) * 4.8 * 5.7 * sin 26°

→ Area (∆PBQ) = 2.4 * 5.7 * sin 26°

→ Area (∆PBQ) = 13.68 * sin 26°

→ Area (∆PBQ) = 13.68 * 0.438

→ Area (∆PBQ) ≈ 6 cm² (Ans.)

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