Question

a fence 2.4m tall,is 10m away from a tree of height 16m.calculate the angle of elevation of the top of the tree from the top of the fence​

Answer 1

Answer:

53.67⁰

Step-by-step explanation:

Give the height of the fence to be 2.4 m tall

Height of the tree = 16m

Horizintal distance from the fence to the tree = 10m

Check the diagram in the attachment.

From the attachment, we will need to first calculate the height AB

AC = AB+BC

Given AC = height of the r=tree = 16m

BC is the height of the fence = 2.4m

16 = AB + 2.4

AB = 16-2.4

AB = 13.6m

Using the SOH CAH TOA trig identity on right angled triangle AEB with AB as the opposite and AB and the adjacent as BE

Using TOA;

tan ∝ = opposite/adjacent = AB/BE

∝ is the angle of elevation of the top of the tree from the top of the fence​.

tan∝ = 13.6/10

tan∝ = 1.36

∝ = tan⁻¹1.36

∝ = 53.67⁰

Hence the angle of elevation of the top of the tree from the top of the fence​ is 53.67⁰