Your classmate is standing on the right side of a monument. She has a piece of rope staked at the base of the monument. She extends the rope to the cardboard square she is holding lined up to the top and bottom of the monument. Use the information in the diagram above to approximate the height of the monument to the nearest tenth.

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oeerivona oeerivona · Answer 1 · 2022-01-25T17:05:10+01:00

The height is the hypotenuse side of the right triangle formed by the

cardboard and the ropes to the top and bottom of the monument.

Correct response:

The possible diagram in the question as obtained from a similar question posted online is attached.

From the diagram, we have;

The angle, θ₁ formed by the rope and the 7.2 ft. segment is given as follows;

[tex] \theta_1 = arctan \left( \dfrac{5.5 \ ft.}{7.2 \ ft.} \right) \approx \mathbf{ 37.376 ^{\circ}}[/tex]

Therefore;

The angle formed by the segment from the cardboard square to the top of the monument, θ₂, is given as follows;

Which gives;

θ₂ ≈ 90° - 37.376° = 52.624°

Therefore;

[tex]tan(\theta_2) = \mathbf{\dfrac{d}{7.2} }[/tex]

Which gives;

d = 7.2 × tan(θ₂)

Therefore;

d = 7.2 × tan(52.624°)

Using trigonometric ratios of tangents of angles that sum up to 90°, we have;

[tex]tan(52.624^{\circ}}) = \mathbf{ \dfrac{72}{55} }[/tex]

Which gives;

Height of the monument, h = d + 5.2

Therefore;

h ≈ 9.43 + 5.2 = 14.63

Learn more about the tangent of angles here;

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