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A person at one end of a 230 foot bridge spots the river’s edge directly below the opposite end of the bridge and fine the angle of depression to be 57 degrees. how far below the bridge is the river

Respuesta :

Answer:

approximately 354.2354.2 feet below the bridge.

Step-by-step explanation:

Let's denote:

d as the distance from the bridge to the river (the height we want to find).

230 feet as the length of the bridge.

Given that the angle of depression is 57∘57∘, we know that:

tan⁡(57∘)=d230tan(57∘)=230d​

We can rearrange this equation to solve for dd:

d=230×tan⁡(57∘)d=230×tan(57∘)

Now, we can calculate dd:

d≈230×tan⁡(57∘)d≈230×tan(57∘)

≈230×1.540≈230×1.540

≈354.2 feet≈354.2 feet

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