To find the height of the sail, which is in the shape of a right triangle, we need to relate the trigonometric functions to the sides of this triangle. We are given an angle, 35 degrees, and we must use the appropriate trigonometric function to find the height.
Let's consider the trigonometric functions:
1. Cosine function (cos) relates the adjacent side (to the angle) over the hypotenuse.
[tex]\[
\cos(35^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}}
\][/tex]
2. Tangent function (tan) relates the opposite side (height in this context) over the adjacent side.
[tex]\[
\tan(35^\circ) = \frac{\text{opposite}}{\text{adjacent}}
\][/tex]
Given the measurements and expressions:
1. [tex]\(\frac{\cos(35^\circ)}{8}\)[/tex]
- This implies some relationship involving cosine spread over 8, but this does not align with seeking the height directly.
2. [tex]\(8 \left(\tan 35^\circ\right)\)[/tex]
- This implies using the tangent function where the height (opposite side) multiplies the adjacent side. Given:
[tex]\[
\tan(35^\circ) = \frac{\text{opposite}}{\text{adjacent}}
\][/tex]
If we multiply both sides by the adjacent side, it becomes:
[tex]\[
\text{opposite} = 8 \left(\tan 35^\circ\right)
\][/tex]
Here, opposite corresponds to the height, and this arrangement correctly relates angle measurement and side lengths to solve for the height.
3. [tex]\(\frac{\tan 35^\circ}{8}\)[/tex]
- This expression does not fit into the typical usage for calculating height using the tangent function correctly.
4. [tex]\(8 \left(\cos 35^\circ\right)\)[/tex]
- This expression suggests using cosine function scaled by 8, which relates to adjacent/hypotenuse relationship and is irrelevant for determining height directly from the angle and base side.
Therefore, the correct choice to find the height of the sail is:
[tex]\[
8 \left(\tan 35^\circ\right)
\][/tex]
Thus, the correct expression showing the height is:
[tex]\[
2
\][/tex]
