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A ladder that is 2020 feet long is leaning against the side of a building. If an angle formed between the ladder and the ground is 7575 degrees, how far is the bottom of a ladder from the base of the building?

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Full solution

Q. A ladder that is 2020 feet long is leaning against the side of a building. If an angle formed between the ladder and the ground is 7575 degrees, how far is the bottom of a ladder from the base of the building?
  1. Calculate Cosine Function: We know the ladder makes a 7575-degree angle with the ground, so we can use the cosine function to find the distance from the bottom of the ladder to the building.\newlinecos⁡(angle)=Adjacent sideHypotenuse\cos(\text{angle}) = \frac{\text{Adjacent side}}{\text{Hypotenuse}}
  2. Plug in Values: Let's plug in the values we know:\newlinecos⁡(75°)=Distance from the building (Adjacent side)20 feet (Hypotenuse)\cos(75°) = \frac{\text{Distance from the building (Adjacent side)}}{20 \text{ feet (Hypotenuse)}}
  3. Calculate Distance: Now, calculate the distance:\newlineDistance from the building = cos⁡(75°)×20\cos(75°) \times 20 feet
  4. Use Calculator: Using a calculator to find cos⁡(75°)\cos(75°):cos⁡(75°)≈0.2588\cos(75°) \approx 0.2588
  5. Multiply Cosine: Multiply the cosine of 7575 degrees by the length of the ladder:\newlineDistance from the building ≈0.2588×20\approx 0.2588 \times 20 feet
  6. Perform Multiplication: Perform the multiplication to find the distance:\newlineDistance from the building ≈5.176\approx 5.176 feet

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