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Item 9 A surveyor is standing 118 feet from the base of the Washington Monument. The surveyor measures the angle of elevation from the ground to the top of the monument to be 78∘. Find the height h of the Washington Monument to the nearest foot. Item 9 A surveyor is standing 118 feet from the base of the Washington Monument. The surveyor measures the angle of elevation from the ground to the top of the monument to be 78∘. Find the height h of the Washington Monument to the nearest foot.

Answer :

calculista

Answer:

555 ft

Step-by-step explanation:

aee the attached figure to better understand the problem

we know that

In the right triangle ABC

[tex]tan(78^o)=\frac{AB}{BC}[/tex] ----> by TOA (oppsoite side divided by the adjacent side)

substitute the given values

[tex]tan(78^o)=\frac{h}{118}[/tex]

solve for h

[tex]h=tan(78^o)(118)=555\ ft[/tex]

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boffeemadrid

The height of the Washington monument is required.

The height of the Washington monument is 555 feet.

Trigonometry

[tex]\theta[/tex] = Angle of elevation = [tex]78^{\circ}[/tex]

b = Distance between the surveyor and the foot of the monument = 118 feet

p = Height of the Washington monument.

From the trigonometric ratios we get

[tex]\tan\theta=\dfrac{p}{b}\\\Rightarrow p=b\tan\theta\\\Rightarrow p=118\tan 78^{\circ}\\\Rightarrow p=555.146\approx 555\ \text{feet}[/tex]

Learn more about trigonometry:

https://brainly.com/question/24349828

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