Question

While standing exactly halfway between two tall trees. Nikki spots a blue jay at the top of one tree and a cardinal at the top of the other, as shown From Nikki is pom‘t of view, the angles of elevation to the blue jay and to the cardinal are 60° and 50", respectively. The trees are 40 m apart.

Answer 1

The height of one trees is 34.64 meters

The height of other tree is 23.83 meters

Explanation:

Given as :

The distance between two trees = d = 40 meters

Nikki is standing at the center O of two tress

The distance between center to one tree = OB = 20 meters

The distance between center to others tree = OD = 20 meters

The angle of elevation of one tree = 60°

The angle of elevation of other tree = 50°

Let The height of one tree = H meters

Let The height of other tree = h meters

Now, From figure

Tan angle =
`(\textrm perpendicular)/(\textrm base)`

Or, Tan 60°=
`(AB)/(BO)`

Or, 1.732 =
`(H)/(20)`

∴ H = 20 × 1.732

i,e H = 34.64 meters

So, The height of one tree = H = 34.64 meters

Again

Tan 50°=
`(CD)/(DO)`

Or, 1.1917 =
`(h)/(20)`

∴ h = 20 × 1.1917

i,e h = 23.83 meters

So, The height of other tree = h = 23.83 meters

Hence, The height of one trees is 34.64 meters and The height of other tree is 23.83 meters Answer