[kashim91]

A vertical pole AB stands on horizontal ground

AB=15

C is a point due south of B
D is a point due east of B

The angle of elevation of A from C is 40
The angle of elevation of A from D is 35

Calculate the distance CD Give your answer to 3 significant figures

[TenOfThem]

Use triangle ABC to find BC
Use triangle ABD to find BD

Use triangle BCD to find CD

All these are right angled triangles
In the first 2 you have an angle and a side so use trig
In the last you have 2 sides so use Pythagoras

[Quantaˌ]

As stated, you need to 'use triangle ABC to find BC', 'use triangle ABD to find BD and then 'use triangle BCD to find CD'. Here is my working out:

BC

tan x°= O/A
tan 40°= 15/BC
tan 40°*BC = 15
BC = 15/tan 40°
BC = 15/0.839
BC = 17.876

BD

tan x°= O/A
tan 35°= 15/BD
tan 35°*BD = 15
BD = 15/tan 35°
BD = 15/0.7002
BD = 21.422

CD

a²+b²=c²
BC²+BD²=CD²
17.876²+21.422²=CD²
319.6+458.9=CD²
778.5=CD²
√778.5=CD
27.9=CD
CD=27.9