Question

a 15.7 meter truck ladder is leaning against a wall like in the diagram below. find the distance d the ladder goes up the wall (above the truck) if the ladder makes an angle of 57°40 with the horizontal. round to one decimal place. 15.7 m d 57°40 question help: message instructor

Explanation:

Step1: Convert the angle from degrees and minutes to decimal degrees

We know that \(1^{\circ}=60'\), so \(40'=\frac{40}{60}\approx0.6667^{\circ}\). Then \(57^{\circ}40'\approx57.6667^{\circ}\)

Step2: Use the sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, the hypotenuse is the length of the ladder (\(15.7\) m) and the opposite side is \(d\). So \(\sin(57.6667^{\circ})=\frac{d}{15.7}\)

Step3: Solve for \(d\)

\(d = 15.7\times\sin(57.6667^{\circ})\)
Using a calculator, \(\sin(57.6667^{\circ})\approx0.844\)
\(d=15.7\times0.844 = 13.3508\approx13.4\)

Answer:

\(13.4\)