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Answer is 8.99, but how tho​

Answer is 8.99, but how tho​-example-1
User Huruji
by
2.4k points

1 Answer

19 votes
19 votes

Answer:

x ≈ 8.99

Explanation:

The mnemonic SOH CAH TOA reminds you of the relationship between trig functions and sides in a right triangle. Here, the geometry of the problem can be modeled by a right triangle. We are given one side and want to find the difference in lengths of the other side for two different angles.

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setup

The tower height is the side opposite the angle of elevation. The distance from the tower to the end of the shadow is the side adjacent to the angle of elevation, so the relevant trig relation is ...

Tan = Opposite/Adjacent

tan(angle of elevation) = (tower height)/(length of shadow)

Solving for the length of shadow, we have ...

length of shadow = (tower height)/tan(angle of elevation)

The difference in shadow lengths is 2x for the two different angles, so we have ...

2x = 24.57/tan(30°) -24.57/tan(45°)

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solution

Dividing by 2 and factoring out the tower height, we have ...

x = 12.285(1/tan(30°) -1/tan(45°)) = 12.285(√3 -1)

x ≈ 8.993244

The value of x is about 8.99.

Answer is 8.99, but how tho​-example-1
User Gokul Kathirvel
by
2.7k points