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You are standing on the Grand View Terrance viewing platform at Mount
Rushmore, 1000 ft from the base of the monument. You look up at the top of
Mount Rushmore at an angle of 24 degrees. About how high is the top of the
mountain from your eye level?

You are standing on the Grand View Terrance viewing platform at Mount Rushmore 1000 ft from the base of the monument You look up at the top of Mount Rushmore at class=

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Answer:

445.23 m.

Step-by-step explanation:

Given,

θ = 24°

B = 1000 ft

Height of the top, H = ?

We know,

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

[tex]\tan 24^\circ = \dfrac{H}{1000}[/tex]

H = 0.44523 x 1000

H = 445.23 m

Height of the top of mount Rushmore is equal to 445.23 m.

Using relations in a right triangle, it is found that the top of the mountain is about 445 ft from your eye level.

What are the relations in a right triangle?

The relations in a right triangle are given as follows:

  • The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.
  • The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.
  • The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.

Hence, in the situation on the image, we have that:

[tex]\tan{24^\circ} = \frac{b}{1000}[/tex]

[tex]b = 1000\tan{24^\circ}[/tex]

[tex]b = 445[/tex]

The top of the mountain is about 445 ft from your eye level.

More can be learned about relations in a right triangle at https://brainly.com/question/26396675

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