Law of Sines/Law of Cosines Word Problem

[Melissaplata]

A vertical flagpole is mounted on a hill that makes a 10° angle with the horizontal. If the sun, shining at an angle of elevation of 70°, makes a 13 foot shadow down the hill, how tall is the flagpole?

 

[MarkFL]

Hello, and welcome to FMH!

Did you draw a diagram? You should have a triangle, where you know the length of the shadow, and the angle opposite that side, and you know the angle opposite the side representing the flagpole. Do you have that yet?

 

[Melissaplata]

It came from a worksheet and the word problem was written exactly like that. The problem is that I don’t know how to draw the triangle in order to be able to use law of sines/cosines.

 

[Dr.Peterson]

Try drawing a diagram of whatever you are able to understand, and we can help you fill in any gaps.

I would start by drawing the (straight, sloped) hillside, at a 10 degree angle; then a vertical pole at the upper end; then a ray of sunlight at a 70 degree angle from the top of the pole to the bottom of the hillside. Then I'd label the shadow (distance on the slope) as 13 feet. At that point, you have a triangle, and can start labeling its angles.