Question

HELP 100 POINTS IF ANSWERED CORRECTLY
A plane takes off, making an angle of a = 8° with the ground. After the plane travels m = three miles along this flight path, how high (in feet) is it above the ground?. (Round your answer to one decimal place.)

Answer 1

Answer:

h = 2204.5 ft

Step-by-step explanation:

To find the height(h) of the plane above the ground, we can use trigonometry, specifically the sine function, since we know the angle of elevation and the length of the hypotenuse.

Given:

• Angle of elevation $a = 8^\circ$
• Hypotenuse $m = 3$ miles
• Opposite to 8° = height(h)

First, we need to convert miles to feet because the height(h) will be in feet.

Since 1 mile is equal to 5280 feet, we have:

$3 \textsf{ miles} \times 5280 \textsf{ feet/mile} = 15840 \textsf{ feet}$

Now, we can use the sine function:

$\sin(a) = \dfrac{\textsf{opposite}}{\textsf{hypotenuse}}$

Substitute the value:

$\sin(8^\circ) = \dfrac{\textsf{height(h)}}{15840}$

Solve for height (h):

$\textsf{height(h)} = \sin(8^\circ) \times 15840$

Using a calculator, we find:

$\textsf{height(h)} \approx \sin(8^\circ) \times 15840$

$\textsf{height(h)} \approx 0.139173101 \times 15840$

$\textsf{height(h)} \approx 2204.501919$

$\textsf{height(h)} \approx 2204.5 \textsf{ feet ( in one decimal place)}$

So, the height(h) of the plane above the ground is:

$2204.5$ feet.