Question

You stand at base camp and look up at the summit of the mountain you are about to climb. The angle of elevation to the top is 15°. You are 5 miles from the point underneath the summit, as shown below.

Which expression below is equivalent to how many feet will you have gained in elevation when you reach the summit?

5 cos (15°) x 5,280
5 cos (15°) ÷ 5,280
5 tan (15°) x 5,280
5 tan (15°) ÷ 5,280

Answer 1

5 tan (15°) x 5,280

Explanation:

You stand at base camp and look up at the summit of the mountain you are about to climb. The angle of elevation to the top is 15°. You are 5 miles from the point underneath the summit, as shown below.

Which expression below is equivalent to how many feet will you have gained in elevation when you reach the summit?

5 cos (15°) x 5,280

5 cos (15°) ÷ 5,280

5 tan (15°) x 5,280

5 tan (15°) ÷ 5,280

Odyssey

Answer 2

its 5tan(15) x 5280

Its a bit difficult to explain because I can't draw out shapes but here's my best explanation:
you set it up as a right triangle, with 15 degrees being your angle, 5 miles as your base (distance from the point underneath summit)(adjacent side,adjacent to angle, in a triangle) and x as your unknown height(opposite side, opposite of angle in triangle). Using SOHCAHTOA, you see that you do not have a value for the hypotenuse, and therefore are left to you use tangent which equals opposite(side) / adjacent (side).


`tan 15 = (x)/(5)`
but you need it in feet, and you were given miles, so you multiply both sides by 5 and convert 1 mi to 5280 feet, so now you have

`5 tan 15= (x)/(5280)`
if you arrange the formula around to solve for x, you get
5tan15 * 5280 = x
* Multiplication, as not to get confused with the variable x

HOPE THAT HELPS