Question

josiah leans a 16-foot ladder against a wall so that it forms an angle of 68° with the ground. how high up the wall does the ladder reach? round your answer to the nearest tenth of a foot if necessary.

Explanation:

Step1: Identify trigonometric ratio

We use sine: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Substitute known values

$\sin(68^\circ) = \frac{x}{16}$

Step3: Solve for $x$

$x = 16 \times \sin(68^\circ)$

Step4: Calculate and round

$x \approx 16 \times 0.9272 = 14.8352 \approx 14.8$

Answer:

14.8 feet