Hard Questionn

[omgineedhelp123]

Wayne is on a hill. He looks up the top of a nearby vertical cliff at an angle of elevation of 36 degrees and looks down the bottom of the cliff at an angle of depression of 47 degrees. Wayne and the cliff are 490 meters apart. What is the height of the cliff?

 

[skeeter]

make a sketch

you'll be using the tangent ratio with two right triangles ... the sides opposite each given angle will be the vertical heights from the base of the cliff to Wayne's position, and from his position to the top of the cliff.

 

[omgineedhelp123]

Can you make a diagram and show me? I still don’t understand. I use the sine law and cousins laws

 

[Mr. Bland]

I've prepared a visualization of the problem as stated:

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Fundamentally, you'll be solving for one of the legs in two different right triangles:

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As @skeeter points out, this can be solved most directly by using the tangent relationships within these triangles.