Question

you are given the guy wire length which corresponds to the hypotenuse.
you are looking for the height of the tower which corresponds to the opposite side.

which equation is used to find the height of the tower?
\\(x = 110 \cos 43^\circ\\)
\\(x = \frac{110}{\cos 43^\circ}\\)
\\(x = 110 \tan 43^\circ\\)
\\(x = \frac{110}{\tan 43^\circ}\\)
\\(x = 110 \sin 43^\circ\\)

round your answer to the nearest whole meter.
the tower is approximately m high.

Explanation:

Identify the given values and trigonometric relationship

We are given that the guy wire length corresponds to the hypotenuse, which is \(110\text{ m}\) based on the selected equation \(x = 110 \sin 43^\circ\). The height of the tower corresponds to the opposite side, denoted as \(x\). The angle of elevation is \(43^\circ\).

Using the definition of the sine function in a right triangle:

$$ \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} $$

Substituting the given values:

$$ \sin 43^\circ = \frac{x}{110} $$

Solve for the height of the tower

To isolate \(x\), we multiply both sides of the equation by \(110\):

$$ x = 110 \sin 43^\circ $$

Calculate the numerical value

Using a calculator to find the value of \(\sin 43^\circ\) (ensuring the calculator is in degree mode):

$$ \sin 43^\circ \approx 0.681998 $$

Now, multiply by \(110\):

$$ x \approx 110 \times 0.681998 \approx 75.0198\text{ m} $$

Round to the nearest whole meter

Rounding \(75.0198\) to the nearest whole number gives:

$$ x \approx 75 $$

Answer:

Question 1

• (A) \(x = 110 \cos 43^\circ\)
• (B) \(x = \frac{110}{\cos 43^\circ}\)
• (C) \(x = 110 \tan 43^\circ\)
• (D) \(x = \frac{110}{\tan 43^\circ}\)
• (E) \(x = 110 \sin 43^\circ\) (Correct answer)

Question 2

The tower is approximately <blank>75</blank> m high.