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The corporate office building is 50m high and angle of elevation at top of building is 52° when seen from a point on level ground. The distance between point and foot of the building is

Respuesta :

Answer:

39.06 m

Step-by-step explanation:

Given that,

Height of the building, h = 50 m

The angle of elevation at top of building is 52° when seen from a point on level ground.

We need to find the distance between point and foot of the building. Let the distance be d. Using trigonometry to find it. So,

[tex]\tan\theta=\dfrac{P}{B}[/tex]

Where

P is perpendicular

B is base.

So,

[tex]\tan\theta=\dfrac{h}{d}\\\\d=\dfrac{h}{\tan\theta}\\\\d=\dfrac{50}{\tan(52)}\\\\d=39.06\ m[/tex]

So, the distance between point and foot of the building is 39.06 m

akposevictor

Applying the trigonometry ratio, TOA, the distance between the point and the foot of the building is: 39.1 m.

Recall:

  • SOH CAH TOA are the common trigonometry ratios that can be used to solve a right triangle.

The information of the building has been sketched in the diagram shown in the image attached below. It shows a right triangle.

  • The distance between the point on the ground and the foot of the building = x (adjacent)
  • Reference angle (∅) = 52°
  • Opposite side = 50 m

Apply the trigonometry ratio, TOA:

tan ∅ = opposite/adjacent

  • Substitute

tan 52 = 50/x

x = 50/tan 52

x = 39.1 m

Therefore, applying the trigonometry ratio, TOA, the distance between the point and the foot of the building is: 39.1 m.

Learn more about trigonometry ratios on:

https://brainly.com/question/8120556

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