Question

isaiah leans a 20-foot ladder against a wall so that it forms an angle of 77° with the ground. how high up the wall does the ladder reach? round your answer to the nearest hundredth of a foot if necessary.

Explanation:

Step1: Identify trigonometric ratio

The ladder is hypotenuse (20ft), height \(x\) is opposite 77° angle. Use sine: \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\).

Step2: Set up equation

\(\sin(77^\circ)=\frac{x}{20}\)

Step3: Solve for \(x\)

\(x=20\times\sin(77^\circ)\)

Step4: Calculate value

\(\sin(77^\circ)\approx0.97437\), so \(x\approx20\times0.97437=19.4874\)

Answer:

19.49