Question

Tamika leans a 30-foot ladder against a wall so that it forms an angle of 65 degrees

with the ground. How high up the wall does the ladder reach? Round your answer to the nearest hundredth of a foot if necessary.

Answer 1

To find the height up the wall that the ladder reaches, we can use trigonometry and the sine function. Using the given angle and length of the ladder, we can calculate the height by dividing the opposite side by the hypotenuse. The ladder reaches a height of approximately 28.00 feet up the wall.

Step-by-step explanation:

To find out how high up the wall the ladder reaches, we can use trigonometry. Since we know the length of the ladder and the angle it forms with the ground, we can use the sine function to calculate the height. The sine of an angle is equal to the opposite side divided by the hypotenuse. In this case, the opposite side is the height of the ladder on the wall, and the hypotenuse is the length of the ladder.

So, we can use the equation:

sin(angle) = opposite / hypotenuse

Plugging in the given values:

sin(65) = height / 30

Solving for height, we have:

height = sin(65) × 30

Using a calculator, we find that the height is approximately 27.98 feet. Rounding to the nearest hundredth of a foot, the ladder reaches a height of 28.00 feet up the wall.