1 a man is standing at the top of a 300ft tower he spots a...

A man is standing at the top of a 300 ft tower. He spots a fire on the ground 250 feet away from the base of the building. What is the angle of depression the man's eyes have to make to look at that fire? Round your answer to the nearest tenth. A) 61.3 B) 50.2 C) 31.7 D) 15.9 2. A kite is flying at an angle of 65 degrees with the ground. A stake in the ground connected to the kite lets out 60 meters of string. Assuming that the string is pulled as tight as it can, how far is the stake from the point on the ground directly beneath the kite? A) 25.3 B) 25.4 C) 17.8 D) 17.7 3. A person standing at the top of a 118 ft lighthouse spots a boat 272 feet away from the base of the lighthouse. 1 hour later, that boat is now 107 feet away. What is the change in the angle of depression from the first sighting of the boat to the second sighting of the boat? Round your answer to the nearest degree. A) 19 B) 26 C) 24 D) 48 4. At noon, a 100 ft tree casts a shadow with an angle of elevation of 16 degrees formed with the ground to the top of the tree. At 3 pm, the angle of elevation has now changed to be 7 degrees. How much longer is the shadow at 3 pm than it was at noon? Round your answer to the nearest foot. A) 465 B) 466 C) 122 D) 123

Transcript

00:01 In this exercise we have four questions.

00:04 We're going to use diagrams to explain all the steps.

00:09 The first question you told that a man is standing at the top of a 300 foot tower.

00:15 So that's the 300 foot tower.

00:19 That's the position of the man.

00:21 And he told that he spots a fire on the ground, 250 feet away from the base of the building.

00:33 So this is the fire.

00:34 So the question is, what is the angle of depression of the man's eyes? so this is the man's view and this is the angle of depression that we're looking for, let's call it x, which is also the angle at the bottom there, x, because these two horizontal lines are parallel and these two angles are alternate interior angles and are congruent.

00:57 So we are trying to find the value of x.

01:00 To find the value of x, we need to use a trigonometric ratio.

01:04 That has the opposite side and the adjacent side.

01:07 That's the tangent.

01:08 So tan x equals 300, the opposite, divided by the adjacent to 150.

01:16 Okay, so let's work this out.

01:18 So 300 divided by 250 is 1 .2.

01:23 And so the x equals the inverse, the turn inverse of 1 .2.

01:29 And the turn inverse of 1 .2 is 50, running to the next nearest 10th, 0 .2 degrees.

01:40 So the correct answer is b.

01:45 In question two we have a kite flying at an angle of 65 degrees with the ground.

01:54 So this is the ground and that's the angle of 65 degrees and so this is where the kite is.

02:04 A stick in the ground is connected to the kite lets out a 60 meters of string so this string is 60 meters and we're going to assume that the string is pulled as tight as it can so we'll be finding how far the stick is to the point on the ground directly beneath the kite so this is the point on the ground directly beneath the kind so we want to get to know how far this stick is from this point here so let's call that point x we're trying to get that length x to get that length x we need a ratio that has the adjacent and the hypotenuse and that's the cosign.

02:46 So the cosine of 65 equals the adjacent x over the hypotenuse 60.

02:54 So x equals 60 cos 65 degrees so let's work this out.

03:02 60 times cos 65 degrees equals 25 .4.

03:11 So the correct answer again is b.

03:15 Go to question number three.

03:18 We've been told that a person is standing at the top of a cliff.

03:22 So that's this point here is the top of the cliff.

03:27 Sorry, a person is standing at the top of a 118 foot lighthouse.

03:32 So this is 118 feet lighthouse and spots a boat that is 272 feet away from the base of the lighthouse.

03:45 So this is how the light moves.

03:49 This is where the boat is and this is where the person is.

03:54 Next, one hour later the boat is now 107 feet away.