1. Brothers Bob and Tom buy a tent that has a center pole of 6.25 feet high. If the sides of the tent are supposed to make a 50deg angle with the ground, how wide is the tent?

2. A swimming pool is 30 meters long and 12 meters wide. The bottom of the pool is slanted so that the water depth is 1.3 meters at the shallow end and 3 meters at the deep end. Find the angle of depression at the bottom of the pool.

Nobody is going to see this but WHY ISN'T THAT WIDTH IN THE PICTURE IS IT THE HYPOTENUSE SO MANY QUESTIONS?!?!?!

1. let the width of the tent be 2x

from my diagram,
tan 50° = 6.25/x
x = 6.25/tan50 = 5.24

So the tent is 2(5.24) appr 10.5 ft wide

2 make a diagram showing a side-view of the pool
Draw a line parallel to the surface of the pool from the shallow end to the deep end, giving you a right-angled triangle
let the angle be Ø
tanØ = 1.7/30 = .05666..
Ø = 3.24°

(notice the width of the pool does not enter the picture)

To find the width of the tent, we can use trigonometric functions.

1. Let's consider the right triangle formed by the center pole, half the width of the tent, and the height of the center pole. In this triangle, the height of the center pole is the side opposite to the angle of 50 degrees, and half the width of the tent is the adjacent side.

2. Using the tangent function, we can write:

tan(50 degrees) = opposite / adjacent

tan(50 degrees) = 6.25 feet / (1/2) * width

3. Rearranging the equation, we get:

width = 6.25 feet / (1/2 * tan(50 degrees))

width ≈ 8.94 feet

Therefore, the width of the tent is approximately 8.94 feet.

Now let's move on to the second question about the swimming pool.
To find the angle of depression at the bottom of the pool, we can use trigonometric functions again.

1. Consider the triangle formed by the shallow end, deep end, and the horizontal line joining them. In this triangle, the difference in water depth between the shallow and deep ends is the opposite side, and the distance between the shallow and deep ends is the adjacent side.

2. Using the tangent function again, we can write:

tan(angle of depression) = opposite / adjacent

tan(angle of depression) = 1.3 meters / 30 meters

3. Rearranging the equation, we get:

angle of depression = atan(1.3 meters / 30 meters)

angle of depression ≈ 2.46 degrees

Therefore, the angle of depression at the bottom of the pool is approximately 2.46 degrees.

To solve both of these problems, we can use trigonometry. Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles.

1. To find the width of the tent, we can use the tangent function. Tangent is the ratio of the length of the side opposite an angle to the length of the adjacent side. In this case, the opposite side is the height of the center pole (6.25 feet) and the adjacent side is half of the width of the tent, since the angle is formed with the ground halfway between the two sides of the tent. So we have:

tan(50 degrees) = opposite / adjacent

tan(50 degrees) = 6.25 / (width / 2)

Now we can solve for the width of the tent:

width / 2 = 6.25 / tan(50 degrees)

width = (6.25 / tan(50 degrees)) * 2

Using a scientific calculator, we can evaluate the expression and find the width of the tent.

2. To find the angle of depression at the bottom of the pool, we can use the inverse tangent function. Inverse tangent, also known as arctan or atan, gives us the angle whose tangent is a given number. In this case, we want to find the angle whose tangent is the ratio of the difference in water depth (3 - 1.3 = 1.7 meters) to the length of the pool (30 meters). So we have:

angle = arctan(1.7 / 30)

Using a scientific calculator, we can evaluate the expression and find the angle of depression at the bottom of the pool.