Question

solve. round answers to the nearest tenth when necessary (one decimal place).
a 35-foot tree casts a shadow. the angle of depression of the sun to the tree is $53^\circ$.
how long is the shadow?
_______ feet

Explanation:

Step1: Identify right triangle sides

Tree height = 35 ft (opposite to $53^\circ$), shadow length = $x$ (adjacent to $53^\circ$)

Step2: Use tangent function

$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$
$\tan(53^\circ) = \frac{35}{x}$

Step3: Rearrange to solve for $x$

$x = \frac{35}{\tan(53^\circ)}$

Step4: Calculate value (use $\tan(53^\circ)\approx1.3270$)

$x \approx \frac{35}{1.3270} \approx 26.4$

Answer:

26.4 feet