Question

Part A: Find the height of the central support ?Part B : Find the distance from point Q to the group when the angle created by the left side of the seating board and the central support is 80 (the length of the dashed line ).

Answer 1

Answer:

A. 1.7 ft

B. 5.8 ft

Explanation:

Part A.

The seesaw forms a triangle as follows

So, we can relate the angle of 25°, the side of 4 ft, and the height of the central support h with the trigonometric ratio sine as follows

$\begin{gathered} \sin25=\frac{\text{ Opposite side}}{\text{ Adjacent side}} \\ \sin25=\frac{h}{4} \end{gathered}$

Solving for h, we get

$\begin{gathered} 4\cdot\sin25=h \\ 4\cdot0.4226=h \\ 1.7\text{ ft = h} \end{gathered}$

Therefore, the height of the central support is 1.7 ft

Part B.

For this part, we have the following diagram

Therefore, there is another triangle formed with hypotenuse d, an angle of 80°, and a side of 1.7ft. Using the trigonometric ratio cosine, we get

$\begin{gathered} \cos80=\frac{\text{ Adjacent side}}{\text{ Hypotenuse}} \\ \cos80=\frac{1.7}{d} \end{gathered}$

Solving for d, we get

$\begin{gathered} d^\cdot\cos80=1.7 \\ d=\frac{1.7}{\cos80} \\ d=\frac{1.7}{0.1736} \\ d=9.8\text{ ft} \end{gathered}$

Then, we want to know the value of x, so we can calculate x as follows

x = 9.8 ft - 4 ft = 5.8 ft

So, the answer for part B is 5.8 ft