Question

find the first mistake in determining the ladder angle when the ladder is 15 ft long and the height against the building is 7 ft. 1. use \\( \sin ( \theta ) = \frac { 7 } { 15 } \\). 2. compute \\( \theta = \arcsin ( \frac { 7 } { 15 } ) = 28.1 ^ { \circ } \\). 3. conclude the ladder makes a \\( 28 ^ { \circ } \\) angle. line 3 no mistakes were made. line 2 line 1

Explanation:

Step1: Analyze the trigonometric ratio

In a right - triangle formed by the ladder (hypotenuse \(c = 15\) ft), the height against the building (opposite side \(a=7\) ft) and the ground (adjacent side \(b\)), if \(\theta\) is the angle between the ladder and the ground, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). But if \(\theta\) is the angle between the ladder and the building (which is more common when talking about the "ladder angle" in such problems), we should use \(\cos\theta=\frac{7}{15}\) (since adjacent side to the angle with the building is \(7\) ft and hypotenuse is \(15\) ft). So line 1 has a mistake in choosing the trigonometric ratio.

Answer:

Line 1