Question

Solve each problem. See Examples 3 and 4. Angle of Depression of a Light A company safety committee has recommended that a floodlight be mounted in a parking lot so as to illuminate the employee exit, as shown in the figure. Find the angle of depression of the light to the nearest minute.

Accepted Answer

Identify the right triangle formed by the floodlight, the point on the ground where the light is aimed (employee exit), and the vertical height of the floodlight from the ground. Label the height of the floodlight as the opposite side and the horizontal distance from the base of the floodlight to the employee exit as the adjacent side of the right triangle. Recall that the angle of depression from the floodlight to the employee exit corresponds to the angle between the horizontal line from the floodlight and the line of sight to the exit, which is congruent to the angle inside the triangle adjacent to the horizontal side. Use the tangent trigonometric ratio, which relates the opposite side and adjacent side: $$	an(	heta) = \frac{	ext{opposite}}{	ext{adjacent}}$$ where $$	heta is $$the angle of depression. Calculate $$	heta by $$taking the inverse tangent (arctangent) of the ratio: $$	heta = 	an$$^{-1}$$\left(\frac{	ext{opposite}}{	ext{adjacent}}ight)$$, then convert the decimal degrees to degrees and minutes to express the angle to the nearest minute.

Solve each problem. See Examples 3 and 4. Angle of Depression of a Light A company safety committee has recommended that a floodlight be mounted in a parking lot so as to illuminate the employee exit, as shown in the figure. Find the angle of depression of the light to the nearest minute.

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Angle of Depression

Right Triangle Trigonometry

Converting Decimal Degrees to Degrees and Minutes