Question

The towers of a suspension bridge reach about 140 mabove the level of the bridge. The angles of elevationof the towers seen from the center the bridge andeither end are 10° and 19° respectively. How long isthe bridge?19°10°10⁰199140m

Answer 1

Solution:

Given:

To get the length of the bridge, we consider the four right triangles A, B, C, and D.

$The\text{ length of the bridge}=x+y+z$

To get x, we use the trigonometric identity of tangent.

$\begin{gathered} tan\theta=\frac{opposite}{adjacent} \\ \\ where: \\ \theta=19^0 \\ opposite=140m \\ adjacent=x \\ \\ Hence, \\ tan19=\frac{140}{x} \\ x=\frac{140}{tan19} \\ x=406.59m \end{gathered}$

To get y, we use the trigonometric identity of tangent.

$\begin{gathered} tan\theta=\frac{opposite}{adjacent} \\ \\ where: \\ \theta=19^0 \\ opposite=140m \\ adjacent=x \\ \\ Hence, \\ tan19=\frac{140}{x} \\ x=\frac{140}{tan19} \\ x=406.59m \end{gathered}$