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Urgent help needed my sister has an exam tomorrow!

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

Reply 1

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

Reply 2

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

(edited 11 years ago)