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The diagram shows an 8-foot ladder leaning against a wall. The ladder makes a 53 degree angle with the wall. Which is closest to the distance up the wall the ladder reaches.

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The diagram shows an 8-foot ladder leaning against a wall. The ladder makes a 53 degree-example-1
User Vamei
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1 Answer

6 votes

Answer:

I’m pretty sure it’s 6.4 feet

Explanation:

Based on the diagram, we can see that we have a right triangle with the ladder, the wall, and the distance up the wall that the ladder reaches.

We know that the ladder is 8 feet long and makes a 53 degree angle with the wall. We can use trigonometry to find the height that the ladder reaches up the wall.

The trigonometric function that relates the angle, the opposite side, and the hypotenuse in a right triangle is the sine function.

In this case, the height up the wall is the opposite side and the ladder is the hypotenuse.

To calculate this value, we first need to find the sine of 53 degrees. The sine function is a trigonometric function that relates the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle. In this case, we want to find the sine of the angle that the ladder makes with the wall, which is 53 degrees.

The sine of an angle is calculated by dividing the length of the side opposite the angle by the length of the hypotenuse. In this case, the length of the side opposite the angle is the height up the wall that the ladder reaches, and the length of the hypotenuse is the length of the ladder, which is 8 feet.

So, we can use the sine function to find the height up the wall as follows:

sin(53) = opposite/hypotenuse

sin(53) = opposite/8

To isolate the value of "opposite" on one side of the equation, we can multiply both sides by 8:

8 * sin(53) = opposite

Now, we can substitute the value of sin(53), which is approximately 0.8, into the equation:

opposite = 8 * sin(53)

opposite = 8 * 0.8

opposite ≈ 6.4 feet

Therefore, the distance up the wall that the ladder reaches is closest to 6.4 feet.

User Sluukkonen
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