Question

a 16 foot ladder leans against a building. if the angle the ladder makes with the ground is 68°, how high up the building does the ladder reach? 39.6 6.0 14.8 13.6

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle where the ladder is the hypotenuse ($c = 16$ feet) and the height up the building is the side opposite the given angle ($\theta=68^{\circ}$). We use the sine function: $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Substitute the values into the sine formula

Let $h$ be the height. Then $\sin(68^{\circ})=\frac{h}{16}$.

Step3: Solve for $h$

$h = 16\times\sin(68^{\circ})$. Using a calculator, $\sin(68^{\circ})\approx0.9272$. So $h=16\times0.9272 = 14.8352\approx14.8$.

Answer:

$14.8$