Question

trig word problems (diagram given) level 1
question
riley leans a 16 - foot ladder against a wall so that it forms an angle of 74° with the ground. whats the horizontal distance between the base of the ladder and the bottom of the wall? round your answer to the nearest hundredth of a foot if necessary.

answer
attempt 1 out of 2
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Explanation:

Step1: Identify the trigonometric ratio

We have a right triangle where the ladder is the hypotenuse (16 feet), the horizontal distance is the adjacent side to the angle \(74^\circ\), so we use the cosine function: \(\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\)

Step2: Substitute the values

\(\cos(74^\circ)=\frac{x}{16}\)

Step3: Solve for \(x\)

Multiply both sides by 16: \(x = 16\times\cos(74^\circ)\)
Calculate \(\cos(74^\circ)\approx0.2756\), then \(x\approx16\times0.2756 = 4.4096\)

Step4: Round to nearest hundredth

\(x\approx4.41\)

Answer:

4.41