SOLUTION: A group of mountain climbers are using trigonometry to find the height of a mountain located in the Rockies. From point A, which is due west of the mountain, the angle of elevation

Question 1058429: A group of mountain climbers are using trigonometry to find the height of a mountain located in the Rockies. From point A, which is due west of the mountain, the angle of elevation to the top is 56 degrees. From point B, which is due east of the mountain, the angle of elevation to the top is 38 degrees. Points A and B are 9.4km apart. Determine the height of the mountain and round to the nearest meter.
This is what I have:
Triangle ABC-- base of triangle is line AB; top point C. Angle of A = 56 degrees, angle of B = 38 degrees, therefore angle C is 86 degrees. (38 + 56 - 180)
Using sine law to find the length of CB (aka "a") c= AB = 9.4km
a/sin A = c/sin C
a/sin(56) = 9.4/sin(86)
a= 9.4 sin(56)/ sin (86)
a= 7.8 km
Now drawing a line from C to AB and calling it h and thus making a right angle triangle I use sine ratio
sin (38)= opposite/hypotenuse
sin (38) = h/7.8
h= 7.8 sin(38)
h= 4.802km or 4802 meters.
Am I correct?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Your strategy for solving the problem is spot on, however, you are off by a few meters because you rounded your intermediate result to too few decimal places.

but

which, to the nearest meter, is 4810 meters.

John

My calculator said it, I believe it, that settles it

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