Find angle BAD of the diagram.

Question

asked Oct 4, 2023 67.8k views

1 Answer

Max Barfuss · Answer 1 · 2023-10-08T19:32:21+0000

∠BAD≈65.22°

Note:

The following formula is tan formula:

$tan(\theta)=(opposite)/(adjacent)$

1) Finding the tan of ∠BAC

$tan(\theta)=(4)/(5)$

$\theta=tan^-1((4)/(5))$

2) Finding the tan of ∠CAD

$tan(\theta)=(3)/(6)$

$\theta=tan^-1((3)/(6))$

3) Add the value of ∠BAC to the value of ∠CAD

tan^-1((4)/(5))+tan^-1((3)/(6))≈65.22°

4) The sum of interior angles in quadrilateral is 360°

Then

tan(∠BAC)+tan(∠ACB)+tan(∠CAD)+tan(∠ACD)=360°

tan^-1((4)/(5))+tan^-1((5)/(4))+tan^-1((3)/(6))+tan^-1((6)/(3))=180°

180°+∠CDA+∠CBA=^?360

180°+90°+90°=^?360°

360°=360°