Suppose that a person with a reach of 27 inches and a shoulder height of 5 feet is standing upright on a mountainside that makes a 62 degrees angle with the horizontal..Can the person touch the mountain?

I said no but idk why?

Don't know about anybody else, but I can't make sense out of your question.

To determine whether the person can touch the mountain, we need to compare the person's reach with the distance between the person's location and the mountain. Let's find the distance using trigonometry:

1. Calculate the height of the mountain (h) using the angle of elevation and the person's shoulder height (SH):
h = SH / tan(angle of elevation)
In this case, SH = 5 feet and the angle of elevation is 62 degrees, so:
h = 5 / tan(62°)

2. Calculate the horizontal distance (d) between the person and the mountain using the height of the mountain (h):
d = h / tan(90° - angle of elevation)
In this case, the angle of elevation is 62 degrees, so:
d = h / tan(90° - 62°)

3. Finally, compare the calculated horizontal distance (d) with the person's reach to determine if they can touch the mountain:
If d is greater than or equal to the person's reach (27 inches), then the person can touch the mountain. Otherwise, they cannot.

You mentioned that the person cannot touch the mountain. Let's calculate h, d, and see if your statement is correct or not.

To determine if the person can touch the mountain, we need to compare the reach of the person with their distance from the mountain.

First, let's convert the shoulder height of the person from feet to inches. Since 1 foot is equal to 12 inches, the shoulder height is 5 feet * 12 inches/foot = 60 inches.

Now, let's visualize the situation. The person is standing upright on the mountainside, and the mountainside makes a 62-degree angle with the horizontal. Let's assume the person is standing at the base of the mountain.

The vertical distance from the person's shoulder height to the top of the mountain can be calculated using trigonometry. We can use the sine function since we have the opposite side (shoulder height) and the hypotenuse (distance from the person to the mountain).

sin(62 degrees) = opposite/hypotenuse
sin(62 degrees) = 60 inches/hypotenuse

Now, we need to find the hypotenuse (distance from the person to the mountain). We can use the trigonometric identity:

hypotenuse = opposite / sin(62 degrees)
hypotenuse = 60 inches / sin(62 degrees)

Using a calculator, we can find the value of sin(62 degrees) to be approximately 0.88.

hypotenuse = 60 inches / 0.88
hypotenuse ≈ 68.18 inches

Since the person's reach is only 27 inches, which is shorter than the calculated hypotenuse of 68.18 inches, the person cannot touch the mountain.

Therefore, your initial answer of "no" is correct.