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Antonia is standing 2.3 miles away from Mt. Drash.  She has to tilt her head upwards 65° in order to look straight at the peak of the mountain.  She wants to figure out how high the mountain is. Write out the equation and find the height of the mountain, rounding to the nearest tenth of a mile.  Show all your work.

 Jan 31, 2019
 #1
avatar+96956 
+3

 

Antonia is standing 2.3 miles away from Mt. Drash.  She has to tilt her head upwards 65° in order to look straight at the peak of the mountain.  She wants to figure out how high the mountain is. Write out the equation and find the height of the mountain, rounding to the nearest tenth of a mile. 

Show all your work.

 

 

 

x is Antonia's eye height off the ground.

M is the height of Mt Drash.

a is the height of the mountain above Antonia's eye level

 

 

\(M = a+x\\~\\ tan 65^\circ = \frac{a}{2.3}\\ a=2.3tan65^\circ\\~\\ M = 2.3tan65^\circ+x \qquad miles\)

 

Antonia's height will be inconsequential so I could have left x out altogether.   :)

 Jan 31, 2019
 #2
avatar+26 
+1

tbh i dont completly understand your explanation but thank you for your help 

BellaNight7310  Jan 31, 2019
edited by BellaNight7310  Jan 31, 2019
 #3
avatar+96956 
+2

Bella you can forget about the x. I was just complicating things unnecessarily.

 

Here is a simpler pic and explanation. 

 

 

 

\(tan 65^\circ=\frac{opposite}{adjacent}\\ tan 65^\circ = \frac{a}{2.3}\\ \text{multiply both sides by 2.3}\\ 2.3 tan 65^\circ = 2.3*\frac{a}{2.3}\\ 2.3 tan 65^\circ = a\\ a=2.3tan65^\circ \qquad miles\\ a=2.3*2.1445 = 4.932\\~\\ \text{The mountain is 4.9km high} \qquad \text{(to 1 decimal place).}\)

 

That was supposed to be miles. I live in Australia where we use km. It was a careless error on my part.  Sorry :)

 

Is that any easier to understand?  Do you have any questions?

Melody  Jan 31, 2019
edited by Melody  Jan 31, 2019
 #4
avatar+26 
+1

no that makes more sense thank you so much

BellaNight7310  Jan 31, 2019

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