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.

Answer 1

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

Answer 2

Thank you so much! I was stuck on that one