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From the top of a lighthouse 175 feet high the angles of depression of the top and bottom of a flagpole are 23° 17' and 42° 38', respectively. How tall is the pole to the nearest tenth of an inch?

I made sure to convert the 175 feet into 2100 inches.

2007-02-15 13:31:01 · 2 answers · asked by spellshell 1 in Education & Reference Homework Help

2 answers

If you can visualize the image, you're drawing a line from the top of the lighthouse to the top of the flagpole, and another line from the top of the lighthouse to the bottom of the flagpole, creating two different triangles. You can find the height of the flagpole through some trig - you'd need to first find out how far the flagpole is from the lighthouse, and then you can solve for the height of the flagpole.

To find the distance, we'll need the angle of depression to the base of the flagpole. You have a triangle where one side is 175 feet (or 2100 inches), and the opposite angle is 42 deg 38 min. You can use tan to find the distance d:

tan 42 deg 38 min = 2100 in/d
d = 2100 in/tan 42 deg 38 min
d = 2281.06 in

Now let's look at the other triangle. If you draw a line parallel to the ground from the top of the flagpole to the lighthouse, you can find the height of the lighthouse minus the height of the flagpole again using tan (we'll call this new height h):

tan 23 deg 17 min = h/2281.06 in
h = (tan 23 deg 17 min)(2281.06 in)
h = 981.6 in

Now if the height from the flagpole to the top of the lighthouse is 981.6 in, then the height of the flagpole is this distance subtracted from 2100 in, or 1118.4 in.

2007-02-16 16:32:19 · answer #1 · answered by igorotboy 7 · 0 1

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2016-09-29 04:22:37 · answer #2 · answered by ? 4 · 0 0

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