Question

In the figure, TF is a tower. The elevation of T from A is x° where tan x = 2/5 and AF = 200m. The elevation of T from B, where AB = 80m, is y°. Calculate :
1. The height of the tower TF.
2. The angle Y, correct to the nearest degree .

Answer 1

• In the figure, TF is a tower. The elevation of T from A is x° where tan x = 2/5 and AF = 200m. The elevation of T from B, where AB = 80m, is y°.
• tan x = TF/AF = TF/200
• But tan x = 2/5. ⇒ TF/200 = 2/5 ⇒ TF = 80 m
• So, the height of the tower is 80 m.
• tan y = TF/BF = TF/ ( AF-AB) = 80 / (200-80) = 80/ 120 = 2 / 3
• y = $tan^{-1}$ ( 2/3) = 33.69⁰

Answer 2

Step-by-step explanation:

figure, TF is a tower. The elevation of T from A is x° where tan x = 2/5 and AF = 200m. The elevation of T from B, where AB = 80m, is y°.

tan x = TF/AF = TF/200

But tan x = 2/5. ⇒ TF/200 = 2/5 ⇒ TF = 80 m

So, the height of the tower is 80 m.

tan y = TF/BF = TF/ ( AF-AB) = 80 / (200-80) = 80/ 120 = 2 / 3

y = tan^{-1}tan

−1

( 2/3) = 33.69⁰