Sheryl is surveying a cliff to determine the elevation from...

Sheryl is surveying a cliff to determine the elevation from the base of a canyon to the top of the cliff. She lays out a line AB that is 225 m in length. She also sights a point C at the base of the cliff. Point D is a point directly above point C, at the top of the cliff. She measures ?CAB to be 43°, ?CBA to be 58°, and the angle of elevation from point A to point D to be 29°. Draw a diagram to model this situation. Determine the height of the cliff.

Transcript

00:01 Here the question is saying that that is selwyn is serving a cliff to determine the elevation from the base of a canyon to the top of the cliff so she lays out a line that is ab that is given having the value so the length is that is 225 meter so consider that this will be that is ab light and further saying that she also sides a point c at the base of the cliff so consider that this will be that is point c and point d will be that is exactly above the point c at the top of the cliff so i will sit at this point d so this will be that is the top of the cliff so now here i will join this a point a to point c and point c to that is point b so you can see that i had got a tangle so this will be representing that is this has the area so that will be representing that is the base of the cliff so that means i can say that that is point a point c and point b so they are lying in same horizontal plane and point d will be that is in the cushion given that is that is representing the top of the cliff so then i will say that if i join this point point c to point d then this angle will be always that is 90 degree so that means i will say that the value of angle acd so that will be that is 90 degree so and similarly if i join that is i was trying to find this angle then this also that is 90 degree so that means i can see that that is be angle b cd this will be that is point c so angle b cd so that will be also 90 degree now further information is given so that is that is the value of angle c a b so that is given so that will be 43 degree so that means this will be that is given 43 degree and this angle also given so that is c b so that is 58 degree and the angle of elevation from point a to point d so that is given so that is 29 degree and now in the question it is asking that we have to find the height of the cliff that means we have to find cd so now i will solve the i will know solve the calculation here after drawing a model drawing a diagram so now here i will write that is the first i'll say that that is angle a c b so that will be written as that is total we know that for triangle the sum of angle will be that is 3 angles is that is 180 degrees and minus subtract angle a having the value that is subtract angle c ab so that is 43 degrees then minus so subtract that is angle c b a so that is 58 degree so simplify it then i'll get this value so angle acb so that is equal to 79 degrees now next step is apply the sign rule so here i write the equation so by sign rule in i'm applying this rule in the triangle acb so it will be written as that is the relation will be so that is ac divided by sign b so that will be equal to that is ab divided by that is sign c now substitute the data here so then i will get the value of ac so it will be written as after putting i will say that it that is ac divided by sign b so that means sign 58 degree so that will be equal to a b that is 225 divided by that is 225 divided by so that is sign c that means sign angle ac b so that is here i will write it is sign 79 degrees so simplify it then i will get the value of ac so that is equal to 194 .38 now next step is that is use the triangle that is acb acd so that means in the diagram you can see that i am using this triangle so in acd here i will say that that is 10 29 degree so that will be written as that is cd divided by ac.

06:27 So now i will say that put the value of ac from this step.

06:34 Simplify it then i will get the value of cd.

06:37 So that is the height of the cliff...

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