Question

If dB=4 and dc=6 find ad

Answer 1

AD=2,667

Explanation:

Given that ABC is a right triangle, right angled at B

BD is the altitude

Since DB and DC are given we can find tan c using right triangle BCD

tan c =
`(DB)/(DC) =(4)/(6)`

Angle ABD is complement of angle A

In triangle ABC , C is complement of angle A

Hence C = angle ABD

`tan ABD = tan C =(AD)/(DB) =(AD)/(4)`

Simplify to get

`AD = 4tanC=4((4)/(6) )\\=(8)/(3)`

Answer 2

see the attached figure
DB = 4 and DC = 6 , We need to find AD

Using Euclid's theorem for the right triangle

∴ DB² = AD * DC

∴ 4² = AD * 6

∴ 6 AD = 16


∴ AD = 16/6 = 8/3 ≈ 2.67