A plane takes off and climbs at a 10º angle. After flying over 12 miles of ground, what will the plane's altitude, h, be? Round to the nearest tenth of a mile.

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Explanation:

A diagram is optional, but I find it helps sometimes. The diagram is shown below.

Opposite the 10 degree angle is h. So we consider h the opposite side.

The hypotenuse is 12. The hypotenuse is always opposite the 90 degree angle.

Apply the sine ratio to solve for h

sin(angle) = opposite/hypotenuse

sin(10) = h/12

12*sin(10) = h

h = 12*sin(10)

h = 2.08377813200317 which is approximate

h = 2.1 miles is the plane's altitude which is also approximate

Side note: 2.1 miles is equal to 11,088 feet (multiply by 5280 to convert from miles to feet).

Not larger or smaller; the areas are the same

Step-by-step explanation:

Recall that the formula for the area of a triangle of base b and height h is

A = (1/2)(b)(h).

In the first case, h = 3 ft and b = 2.5 ft.  This results in an area of 3.75 ft^2.

In the second case, h = 2.5 ft and b = 3 ft.  The area is the same:  3.75 ft^2.

This is because A = (1/2)(b)(h) has the same value regardless of the order in which b and h  are used as multipliers.

There is no difference in the areas of the two signs.  The areas are the same.