Kayson is looking at two buildings, building A and building B, at an angle of elevation of 59°. Building A is 40 feet away, and building B is 60 feet away. Which building is taller and by approximately how many feet?
Building A; it is around 66.57 feet taller than building B
Building A; it is around 33.29 feet taller than building B
Building B; it is around 66.57 feet taller than building A
Building B; it is around 33.29 feet taller than building A

Trigonometry is mainly concerned with specific functions of angles and their application to calculations. Trigonometry deals with the study of the relationship between the sides of a triangle (right-angled triangle) and its angles.

For the given situation,

The diagram below shows the Kayson at C and the two buildings at A and B.

An angle of elevation of both building A and B is 59°.

In the diagram, the hypotenuse touches the top of building A and keeps ongoing at the same angle to building B, further away.

When things are nearer they appear bigger, hence, if the buildings have the same angular elevation from the same spot, the taller building is further away.

Distance between Kayson and building A is 40 feet and the distance between Kayson and building B is 60 feet.

The height of the building A is obtained by trigonometric ratio,

[tex]tan \theta = \frac{opposite}{adjacent}[/tex]

Here, opposite side = h1, adjacent = 40, θ = 59°

⇒ [tex]tan 59 = \frac{h1}{40}[/tex]

⇒ [tex]1.6642(40)=h1[/tex]

⇒ [tex]h1=66.57[/tex]

The height of the building B is obtained by trigonometric ratio,

Here, opposite side = h2, adjacent = 60, θ = 59°

⇒ [tex]tan 59 = \frac{h2}{60}[/tex]

⇒ [tex]1.6642(60)=h2[/tex]

⇒ [tex]h2=99.86[/tex]

Difference, [tex]h2-h1=99.86-66.57[/tex]

⇒ [tex]33.29[/tex]

Hence we can conclude that option (D) building B; it is around 33.29 feet taller than building A is the correct answer.

Learn more about trigonometry here

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