Posted by **Kourt** on Monday, November 22, 2010 at 10:39pm.

In traveling across flat land, you notice a mountain in front of you. Its angle of elevation to the peak is 3.5 degrees. After you drive 13 miles closer to the mountain, the angle of elevation is 9 degrees. Approximate the height of the mountain.

- MATH -
**Reiny**, Monday, November 22, 2010 at 10:59pm
make a sketch

draw the height of the mountain as AB

C is the point of first observation (3.5°)

D is the point of second observation (9°)

angle B = 90° , CD=13, angle C=3.5, and angle ADB=9°

In triangle ACD, angle CDA = 171° and angle CAD=5.5°

by the Sine Law:

AD/sin 3.5 = 13/sin 5.5

AD = 13sin3.5/sin5.5 = 8.28029

now in the right-angled triangle,

sin 9° = AB/AD

AB =8.28029sin9 = 1.295 miles

check my arithmetic

- MATH -
**Kourt**, Monday, November 22, 2010 at 11:05pm
Thank you so much! I was stuck on that one

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