A ship sees a 100-ft tall lighthouse in the distance. Using his sextant, the ship's navigator determines that the angle of elevation from the ship to the top of the lighthouse is 25 degrees. How far is the ship from the lighthouse???
2007-04-24 14:13:23 · 8 answers · asked by Juan C 6 in Science & Mathematics ➔ Mathematics
We first need to assume that the ship is going at a right angle to the base of the lighthouse.
If we draw a triangle, we would have the ship having a line of sight to the top of the lighthouse. This serves as the hypotenuse. The straight line distance from the ship to the base of the lighthouse is the base of the triangle, and the height of the triangle is the lighthouse.
So, we know the height is 100ft, and the angle by the ship is 25°, and we are looking for the distance to the base, which we will use as x.
So we know an angle, the opposite side from that angle, and also the adjacent side from that angle. This is where the tangent function comes into play because according to SOH - CAH - TOA...tangent = opposite / adjacent.
So we set it up as tan(25°) = 100 / x.
We do algebra to solve for x which gives us = 100/tan(25°). Then by using the calculator to get an estimate, we get a distance of 214.4506920, so about 214.5 feet.
2007-04-24 14:32:38 · answer #1 · answered by pecosbill2000 3 · 1⤊ 0⤋
Let x be the distance of ship from lighthouse.
Form a right-angle triangle with the lighthouse being the opposite, x being the adjacent.
tan 25 = 100/x
x = 100 / tan25
x = 214.45ft
2007-04-24 14:19:43 · answer #2 · answered by QiQi 3 · 1⤊ 0⤋
You draw out the picture and see that it forms a right triangle. You realize that you have the angle of elevation and the height of the side adjacent to the 90 degree angle is 100 ft tall. Using the tangent function, you realize this equals opposite over adjacent. Thus, tan 25 degrees = 100/x. Once you reconfigure this, you get 100 divided by the tangent of 25 degrees to get approximately 214.45 ft. You could also add 25 and 90 to get 115 and subtract this from 180 to attain 65 (the other angle in the triangle). Tan 65 =x/100, and this gives you the same answer of approximately 214.45.
2007-04-24 14:32:00 · answer #3 · answered by mean streak 2 · 1⤊ 0⤋
tan 25 = 100/d
0.4663 = 100/d
d = 214.5 ft
lighthouse is opposite angle and distance is the adjacent side, so tangent is used. tan = opp/adj
2007-04-24 14:17:38 · answer #4 · answered by richardwptljc 6 · 1⤊ 0⤋
x = distance to lighthouse
hen x/100 = cot 25
x= 100 cot25
x = 100*2.1445 = 214.45 feet
2007-04-24 14:21:20 · answer #5 · answered by ironduke8159 7 · 0⤊ 0⤋
Drink some quarts of water and also you need to bypass after him with your self-contained water cannon. the perspective of melancholy is arctan(3/10). in case you draw a triangle with one leg one hundred ft from Mr. M to the sting of the college, and one leg 30 ft intense, the perspective whose vertex is Mr. M. (and whose hypotenuse is the line of hearth) has a tangent of three/10. because you're on precise of the construction, your perspective of melancholy is a similar (alt interior angles of a line connecting 2 parallel lines deal).
2016-12-04 19:50:17 · answer #6 · answered by yau 4 · 0⤊ 0⤋
Ok, let's use trigonometry :
tan(25) = 100 / x
X = 214.45 ft
Hope that helps
2007-04-24 14:17:51 · answer #7 · answered by anakin_louix 6 · 1⤊ 0⤋
tan25=100/x
x=100/tan25
x=214.450ft
2007-04-24 14:18:39 · answer #8 · answered by Anonymous · 1⤊ 0⤋