From a boat on the river below a dam, the angle of elevation to the top of the dam is 22°23'. if the dam is 2457 feet above the level of the river, how far is the boat from the base of the dam (to the nearest foot)?

This illustrates a right triangle.
Given:
a(height) = 2457 ft.
∠A = 22°23' ; which is the elevation and reflects the a(height)

Find:
b(base)

Solution:

Using the law of cosine, specifically tan∠ = opposite side÷adjacent side
By analysis, tan∠A = a÷b

Since we are finding b, the formula will be derived into:
b = a÷tan∠A

Find b(base):
b = 2457 ft. ÷ tan22°23' ; substituting the numbers
b ≈ 5,966.05 ft. ; Final Answer

53 miles

Step-by-step explanation:

I'm going to assume "$0.25 for each time" is "$0.25 per mile."

$1.75 is the flat fee. It costs 25 cents for each mile. We can represent this as:

1.75 + 0.25m

The sum of this equation has to be less than or equal to $15. We can display this as:

1.75 + 0.25m ≤ 15.

To solve, we must first isolate 0.25m. To do this, we subtract 1.75 from each side.

0.25m ≤ 15 - 1.75

0.25m ≤ 13.25.

Now, we must isolate the variable 'm' to determine how many miles Eddie can travel. To do this, we divide 0.25 from each side.

m ≤ 13.25 / 0.25

m ≤ 53.

Therefore, Eddie can travel 53 miles if he has $15 to spend.