A 36-ft ladder leans against a building so that the angle between the ground and the ladder is 79°. How high does the ladder reach up the side of the building? (Round your answer to four decimal places.) 

To solve this problem, we will use trigonometry. The ladder forms a right triangle with the ground and the building. Let's define the terms:

- \( L = 36 \) ft (length of the ladder, which is the hypotenuse of the right triangle)
- \( \theta = 79^\circ \) (angle between the ground and the ladder)
- \( h \) is the height the ladder reaches up the side of the building (opposite side to the angle)

We will use the sine function, which relates the opposite side to the hypotenuse in a right triangle:

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]

Substituting the given values:

\[
\sin(79^\circ) = \frac{h}{36}
\]

Now, solve for \( h \):

\[
h = 36 \times \sin(79^\circ)
\]

Let's calculate this value.The height that the ladder reaches up the side of the building is approximately \(35.3386\) feet, rounded to four decimal places.

Would you like further details or have any questions?

Here are some related questions you might find interesting:

1. What is the distance from the base of the building to the bottom of the ladder?
2. How would the height change if the ladder's angle with the ground were different?
3. Can we calculate the angle if the height reached by the ladder is known?
4. What is the relationship between the angle, ladder length, and the height reached?
5. How does trigonometry help in solving real-life problems like this?

**Tip:** In right triangles, using trigonometric functions such as sine, cosine, and tangent can help you find unknown lengths or angles effectively.

A 36-ft ladder leans against a building so that the angle between the ground and the ladder is 79°. How high does the ladder reach up the side of the building? (Round your answer to four decimal places.)

Learn how to calculate the height a 36-ft ladder reaches up the side of a building when it makes a 79° angle with the ground. This trigonometry problem involves the sine function and is suitable for students in Grades 9-11. The solution is detailed and rounded to four decimal places.

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