# You lean a ladder 6.7 meters long against the wall. It makes an angle of 63° with the level ground. How high up is the top of the ladder?

I found:

Consider the diagram:

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To find how high up the top of the ladder reaches, you can use trigonometric functions, specifically the sine function. Since the ladder, the wall, and the ground form a right triangle, you can use the sine function, which relates the length of the side opposite an angle to the length of the hypotenuse.

Given that the ladder is 6.7 meters long and forms an angle of 63° with the ground, you can use the sine function:

[\sin(63°) = \frac{{\text{{height}}}}{{\text{{length of ladder}}}}]

Solving for the height:

[\text{{height}} = \text{{length of ladder}} \times \sin(63°)]

Substitute the values:

[\text{{height}} = 6.7 \times \sin(63°)]

Calculate the value:

[\text{{height}} \approx 6.7 \times 0.891]

[\text{{height}} \approx 5.9677]

So, the top of the ladder reaches approximately 5.9677 meters up the wall.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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