Solve each problem. See Examples 3 and 4. Angle of Depression ...

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

Welcome back. Everyone in this problem, Edward is standing near the edge of a cliff that sites a canoe that is 156.34 ft from the bottom of the cliff. Calculate the angle of depression of the line of sight of Edward and round your answer to the nearest minute, considering the height of Edward as negligible for our answer choices. A is 34 degrees, 43 minutes. B is 33 degrees, 11 minutes, C is 36 degrees, 27 minutes and D is 38 degrees 55 minutes. Now, for us to solve this problem, let's try to draw our own diagram. So we're talking about a man named Edward standing at the top of a cliff and we already know that this cliff, the height of this cliff is 108. ft. Ok. And we also know that the canoe is 156.34 ft from the bottom of the cliff. So starting from the bottom of the cliff to the canoe would have been 156.34 ft. Ok. And we know that we're trying to calculate the angle of depression of the line of sight of Edward. Now the angle of depression would be the angle at which Edward is looking down. Note that Edward's line of sight is a horizontal line. Ok. Uh So let me identify that line of sight here, line of site. So the angle of depression would be the angle between the line of sight and his direct view onto the canoe. Now notice that our angle of depression is alternate to the anger that is formed between the Cano and Edward. In other words, if I were to identify it here, that means both of those angles would be equal. So we have an angle inside the triangle that's formed with the views. And we know that from the canoe to the bottom of the cliff, that would make a right angle with the bottom of the cliff going up to Edward. So here we have a diagram and if we want to find that angle of depression we can use or we can solve for the angle inside or triangle. Now, what do we know here about the angle inside our diagram? Well, for this angle, the side opposite to it would have been 108.32 ft, the height of the cliff and the side adjacent to it would have been 156.34 ft. That is the distance of the canoe to the bottom of the cliff Now let's think about it since it forms a right angle to triangle, what trigonometric ratio relates the adjacent side to the opposite. Of course, that would be the tangent. So recall that the tangent of an angle is the ratio of its opposite side to its adjacent side. So what this tells us then is that the tangent for our angle that we want the angle of depression equals the opposite side 108.32 divided by the adjacent side, 156.34. That means our angle would be equal to the inverse tangent of our co that is 108.32 divided by 156.34. And when you put that into your calculator, you'll find that your angle equals degrees 42 minutes and 58 seconds. But again, recall that we want our answer to the nearest minute. So rounding 34 degrees, 42 minutes and 58 seconds to the nearest minute would give us approximately 34 degrees and minutes. When we look back on our answer choices, that would have been answer choice. A thanks a lot for watching everyone. I hope this video helped.

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.

Key Concepts

Angle of Depression

Right Triangle Trigonometry

Converting Decimal Degrees to Degrees and Minutes

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