Question

7. What is the value of x to the nearest foot? *

8000 ft
40°
X
6713 ft
9534 ft
10,443 ft
12,445 ft

Answer 1

The answer is 6713 ft

Answer 2

The value of x to the nearest foot in the right-angled triangle, given a height of
`8000` ft and an angle of
`40` degrees between the hypotenuse and base, is approximately
`10,421` ft, closest to option C.

To find the value of x, we can use the cosine function, as the cosine of an angle in a right-angled triangle is defined as the ratio of the adjacent side to the hypotenuse.

In this case, for the angle between the hypotenuse and the base (
`40` degrees), the cosine function is given by:

`\[ \cos(40^\circ) = \frac{{\text{base (adjacent)}}}{{\text{hypotenuse}}} \]`

Given that the height is
`8000` ft and using the cosine formula:

`\[ x = \frac{{\text{height}}}{{\cos(\text{angle between hypotenuse and base})}} \]`

`\[ x = \frac{{8000}}{{\cos(40^\circ)}} \]`

Now, calculate this expression to find the value of x to the nearest foot.

`\[ x \approx \frac{{8000}}{{0.766}} \]`

`\[ x \approx 10420.732 \]`

Rounding to the nearest foot, the value of x is approximately
`10,421` feet. Therefore, the closest option is C.
`10,443` ft.