While traveling across flat land, you notice a mountain directly in front of you. The angle of elevation to the peak is 2.5 degrees. After you drive 17 miles closer to the mountain, the angle of elevation is 9 degrees. Approximate the height of the mountain.
2007-10-14 08:49:34 · 3 answers · asked by yoursmilemakesme 2 in Science & Mathematics ➔ Mathematics
Sketch right angled triangle ADB
Right angled at D
/_ ABD = 2.5°
BC = 17
CD = x (where C lies on BD)
AD is vertical = h
/_ACD = 9°
tan 2.5° = h / (17 + x)
h = tan 2.5°(17 + x)
tan 9° = h/x
h = tan 9° x
tan 2.5° (17 + x) = tan 9° x
17 tan 2.5° + x tan 2.5° = x tan 9°
17 tan 25° = x (tan 9° - tan 2.5°)
7.93 = x (0.115)
x = 69
tan 9° = h / x
h = (tan 9°) (69)
h = 10.9 miles
h = 57552 ft
2007-10-18 06:59:14 · answer #1 · answered by Como 7 · 0⤊ 0⤋
Draw the picture. If m = height of mountain and x = distance on ground from mountain to the 9 degree angle, then (x+17) = ground distance from mountain to the 2.5 degree angle.
tangent = opp leg / adj leg so
tan 2.5 = m/(x+17)
tan 9 = m/x
Cross multiply these (put 1 under the tan's) to get
m = (x+17) tan 2.5
m = x tan 9
So since both equal m,
(x+17) tan 2.5 = x tan 9
Look up or calculate the tangents and plug them in to get x, then multiply x by tan 9 to get m
2007-10-14 09:05:29 · answer #2 · answered by hayharbr 7 · 0⤊ 0⤋
http://photobucket.com
http://i55.photobucket.com/albums/g149/delta_bravo_1kilo/My_Pictures/homework.jpg
2007-10-14 09:15:30 · answer #3 · answered by JavaScript_Junkie 6 · 0⤊ 0⤋