MIDTERM EXAM 1. A flagpole 10 ft. tall stands on top of a...

MIDTERM EXAM 1. A flagpole 10 ft. tall stands on top of a building. From a point in the same horizontal plane with the base of the building, the angles of elevation of the top and the bottom of the flagpole are 60° and 50° respectively. How high is the building? 2. A 30 ft. ladder makes an angle of 60° with the horizontal when it reaches a given spot on a wall. What angle will a 35 ft. ladder make with the horizontal if it reaches the same spot? 3. From a given position A, an observer notes that the angle of elevation of a rock is 45°. After walking at point B 100 ft. towards the rock, up a slope of 30°, he finds the angle of elevation to be 70°. Find the vertical distance of the rock above each point of observation. 4. The diagonals of a parallelogram are 10" and 18" respectively, intersect at an angle of 50°. Find the longer side of the parallelogram. 5. A ladder, 20 ft. long is set with one end at a horizontal distance of 7 ft. from a sloping wall. The other end of the ladder reaches 15 ft. up the face of the wall. What angles does the wall makes with the ladder?

Transcript

00:01 Hi in this question we have a point a and a rock right so here we have a rock i suppose its hide is a edge it is rock all right okay so the angle of elevation of the rock let me draw it once again so yeah the angle of elevation of the rock peak from is given as 45 degree all right now it is given that on walking 100 feet 100 feet with a slope of 30 degree with slope of 30 degree towards the of a that means 30 degree is somewhere here so there's a point b all right which is when we walk 100 feet so the distance so the red distance will be hundred feet all right the slope of 30 degree there is a point b which is this all right so it is given in the question from point b the angle of elevation to the peak of the rock is 70 degree all right it is 70 degree okay yeah so we need to find the vertical distance of the rock from each point of observation so we need to find out the height of the rock right we need to find out the height of the rock from point a as well as from point b right vertical distance there is nothing but this height so let's suppose from b we have it is h1 and this height would be s2 all right okay so using a basic trigonometry we can easily find out the value of h1 and s2 all right now looking for let's name this point as c and it is a d.

02:22 Alright so in triangle acd we have a i can say that 10 of 45 degree 10 of 45 degree we have nothing but s2 upon base all right we can say that which is base is nothing but ac right so 10 of 45 is nothing but one we have h2 upon ac.

02:48 All right so as a result of that we got ac ac equal to s2 all right we have ac equal to s2 all right so s2 and ac both are equal to each other now using this triangle which is ab and name it as e right in triangle abe all right you can say that you can say that using cost relation.

03:19 All right.

03:19 So it is 30 degree, nothing about 30 degrees.

03:22 So using course of 30, cross 30, we have base upon hypotenous.

03:28 So our base is nothing but a .e and a .e divided by hypotenous, which is nothing about 100 feet.

03:38 All right.

03:39 So cause study is nothing but root 3 by 2.

03:43 Right, let me write it over here.

03:46 We'll 3 by 2.

03:47 We have a .e.

03:49 By 100 all right so a would be on simplifying it we get 50 root 3 all right so we have the value of a yes 50 03 all right okay so now in triangle now all right so it is this this is it now in triangle a now in triangle b d and name it as f this point now in triangle bd and name it as f this one now in triangle b but we have a 10 of 70 degree is nothing but h1 upon bf, right? look, bf is equal to ec because it is rectangle and the opposite sides of rectangle is equal, right? so h1 upon bf, we can write it as 10 of 70 equal h1 upon ec.

04:52 Alright and ec is nothing but we can write it ec is nothing but 10 of 70 we can say h1 upon ec is nothing but ae this whole ac minus ae alright it is nothing but ec alright it is nothing but ec so we can say ec as ac minus ae all right now from from these two questions we have ac and ae value now if we put up here we get 1070 h1 upon as ec we have ac as s 2 and the minus a ees 50 row 3 50 all right so this is the scenario all right so now okay now in order to find out ec so we need to find out the value of h1 and s2 all right so we have this expression for h1 and this expression for h2.

06:04 We need to find out the value of ac.

06:06 Like what is ac? if we can able to find out ac, then we will eventually find out more thing than all right.

06:16 Okay, let's find out this.

06:19 So in this triangle abe, we have 30 degree inclination and 100 feet high.

06:28 So what we can see there, like 100 cost of 30 would be this.

06:35 Alright, yeah.

06:36 100 into course of 30 would be this, a .e.

06:40 Alright, now calculate a .e.

06:42 From here.

06:43 So, let me change the ink.

06:45 So in triangle ae .b.

06:49 So in triangle ae .b.

06:52 What we have? aeb.

06:55 All right.

06:56 We have aeb.

06:58 We have a, v, e, and 100 feet, all right, 30 degree, okay.

07:09 Okay, let me draw this triangle.

07:15 All right, so we have a, e, b.

07:19 Okay, so it is 30 degree, it is 100 feet, hypotenuse, and we don't know ae.

07:27 So we can say that e is nothing but ae is actually nothing but 100 into cost of 30, right? 100 into possible 30.

07:39 It is nothing but that.

07:41 Alright...

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