A ladder is leaning against a wall. The foot of the ladder is 6.5 feet from the wall. The ladder makes an angle of 74° with the level ground. How high on the wall does the ladder reach? (Round your answer to the nearest hundredth.)Question 2Answera.18.51 ft. b.29.12 ft. c.15.36 ft.d.22.67 ft.
Question
A ladder is leaning against a wall. The foot of the ladder is 6.5 feet from the wall. The ladder makes an angle of 74° with the level ground. How high on the wall does the ladder reach? (Round your answer to the nearest hundredth.)Question 2Answera.18.51 ft. b.29.12 ft. c.15.36 ft.d.22.67 ft.
Solution
To solve this problem, we can use the trigonometric function sine. The sine of an angle in a right triangle is defined as the length of the opposite side divided by the length of the hypotenuse. In this case, we want to find the height of the wall, which is the opposite side of the angle, and we know the distance from the wall to the foot of the ladder, which is the adjacent side.
The formula is: sin(angle) = opposite/hypotenuse
We can rearrange the formula to find the opposite side (height of the wall): opposite = sin(angle) * hypotenuse
Here, the angle is 74 degrees and the hypotenuse is the length of the ladder, which is 6.5 feet.
So, the height of the wall is: opposite = sin(74) * 6.5
Using a calculator, sin(74) is approximately 0.96126.
So, the height of the wall is approximately: opposite = 0.96126 * 6.5 = 6.248 feet
Rounding to the nearest hundredth, the height of the wall is approximately 6.25 feet.
Therefore, none of the provided options (a.18.51 ft., b.29.12 ft., c.15.36 ft., d.22.67 ft.) are correct.
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