IDNLearn.com is the place where your questions are met with thoughtful and precise answers. Our platform is designed to provide trustworthy and thorough answers to any questions you may have.

The sail of a boat is in the shape of a right triangle. Which expression shows the height, in meters, of the sail?

A. \(\frac{\cos 35^{\circ}}{8}\)
B. \(8\left(\tan 35^{\circ}\right)\)
C. \(\frac{\tan 35^{\circ}}{8}\)
D. [tex]\(8\left(\cos 35^{\circ}\right)\)[/tex]


Sagot :

To determine which expression shows the height of the sail in a right triangle, let's break down the problem.

In this scenario, the sail forms a right triangle where we need to find the height (opposite side) using the given angle (35°) and a known side (which would typically be the base or the hypotenuse).

Let's denote:
- \( \theta \) = 35° (the given angle)
- \( \text{height} \) = the opposite side to the angle \(\theta\)
- \( \text{base} \) = the side adjacent to the angle \(\theta\) (given to be 8 meters here)

The trigonometric function that relates the opposite side and the adjacent side with the angle is the tangent function:
[tex]\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \][/tex]
Here, \(\theta = 35^\circ\), the opposite side is the height we want to find, and the adjacent side is 8 meters.

We can set up the equation using the tangent function:
[tex]\[ \tan(35^\circ) = \frac{\text{height}}{8} \][/tex]

To find the height, solve for it by multiplying both sides of the equation by 8:
[tex]\[ \text{height} = 8 \cdot \tan(35^\circ) \][/tex]

Thus, the correct expression that shows the height, in meters, of the sail is:
[tex]\[ 8 \left( \tan(35^\circ) \right) \][/tex]

Among the given choices, this matches the second option:
[tex]\[ 8\left(\tan 35^\circ\right) \][/tex]

So, the correct answer is:
[tex]\[ 8\left(\tan 35^\circ\right) \][/tex]