Question

if a 20 foot ladder is leaned against a wall at a 71° angle with the ground, how high above the ground is the top of the ladder? feet

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle where the ladder is the hypotenuse ($c = 20$ feet), the height above the ground ($h$) is the side opposite the given angle ($\theta=71^{\circ}$). Using the sine function: $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Substitute the values into the formula

Substitute $\theta = 71^{\circ}$ and $c = 20$ into $\sin\theta=\frac{h}{c}$. So, $h = c\times\sin\theta$.

Step3: Calculate the value

We know that $\sin(71^{\circ})\approx0.9455$. Then $h=20\times\sin(71^{\circ})\approx20\times0.9455 = 18.91$.

Answer:

$18.91$