Question

a 10.5 - m fire truck ladder is leaning against a wall. find the distance d the ladder goes up the wall (above the fire truck) if the ladder makes an angle of 50° 35′ with the horizontal. d ≈ 8.1 m (simplify your answer. type an integer or a decimal. round to the nearest hundredth.)

Explanation:

Step1: Convert angle to decimal degrees

First, convert $50^{\circ}35'$ to decimal degrees. Since $1^{\circ} = 60'$, then $35'=\frac{35}{60}\approx0.5833^{\circ}$, so $50^{\circ}35'\approx50.5833^{\circ}$.

Step2: Use sine function

In a right - triangle formed by the ladder, the wall and the ground, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, the hypotenuse is the length of the ladder $l = 10.5$ m and the opposite side to the angle $\theta$ (the angle between the ladder and the horizontal) is $d$. So $\sin(50.5833^{\circ})=\frac{d}{10.5}$.

Step3: Solve for $d$

$d = 10.5\times\sin(50.5833^{\circ})$. Using a calculator, $\sin(50.5833^{\circ})\approx0.7724$, then $d=10.5\times0.7724 = 8.1102\approx8.11$ m.

Answer:

$8.11$ m