Question

a 16 - ft ladder leans against a building so that the angle between the ground and the ladder is 79°. how high does the ladder reach on the building? ft question help: video submit question

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle where the ladder is the hypotenuse ($c = 16$ ft) and the height on the building is the side opposite the given angle ($\theta=79^{\circ}$). We use the sine function: $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Solve for the opposite side

Let $h$ be the height. Then $\sin(79^{\circ})=\frac{h}{16}$. So, $h = 16\times\sin(79^{\circ})$.
Using a calculator, $\sin(79^{\circ})\approx0.9816$.
Then $h = 16\times0.9816=15.7056$.

Answer:

$15.7$ ft (rounded to one decimal place)