Answered

IDNStudy.com, ang iyong gabay para sa mga sagot ng eksperto. Alamin ang mga maaasahang sagot sa iyong mga tanong mula sa aming malawak na kaalaman sa mga eksperto.

At a point 42.3 feet from the base of a building, the angle of elevation of the top is 75º. How tall is the building?   ​

Sagot :

UK2019idn

✏️TRIGONOMETRY

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

[tex]\underline{\mathbb{PROBLEM:}}[/tex]

  • At a point 42.3 feet from the base of a building, the angle of elevation of the top is 75º. How tall is the building?

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

[tex]\underline{\mathbb{ANSWER:}}[/tex]

[tex]\qquad\LARGE\rm»\:\: \green{≈157.87 \: feet}[/tex]

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

[tex]\underline{\mathbb{SOLUTION:}}[/tex]

- We can represent the angles and the sides of a right triangle.

  • 75° is the referred angle.
  • 42.3ft. is the adjacent.
  • The height of the building is the opposite.

- Using trigonometry, we can solve for the height by using the tangent ratio. Let x be the height of the building.

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

  • [tex] \tan75 \degree = \frac{x}{42.3} \\ [/tex]

  • [tex]42.3 \cdot \tan75 \degree = \frac{x}{ \cancel{42.3}} \cdot \cancel{42.3} \\ [/tex]

  • [tex]157.87 ≈ x[/tex]

[tex]\therefore[/tex] The height of the building is 157.87 feet.

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

#CarryOnLearning

View image UK2019
Maraming salamat sa iyong pakikilahok. Patuloy na magbahagi ng iyong mga ideya at kasagutan. Ang iyong kaalaman ay mahalaga sa ating komunidad. Bawat tanong ay may sagot sa IDNStudy.com. Salamat sa pagpili sa amin at sa muling pagkikita.