Posted by **Dana** on Saturday, July 21, 2012 at 5:13pm.

A flagpole stands at a right angle to the horizontal at the bottom of a slope. The slope has an incline of 8° with the horizontal. The flagpole casts a 20 meter long shadow up the slope. The angle of elevation of the sun is 17°. Determine the height of the flagpole.

- math -
**MathMate**, Saturday, July 21, 2012 at 6:56pm
The key to solving this kind of problems is to draw a diagram, and name the unknowns. After that, state the formulas that relate the unknown(s). Some times at the end, only one unknown is left, and you can therefore solve the problem.

Let A be the end of the shadow, and C be the bottom of the pole on the slope.

D be a point directly below C on a horizontal plane at the same level as A (i.e. on a horizontal surface below the slope).

Let B be the top of the pole.

Let

The height of the pole is x (=distance CB).

The distance between C and D be y.

From the definition of sine, we have

CD=y=20 sin(8°) and

From the definition of cosine, we have

AD=20 cos(8°)

and from the definition of tangent,

BD=AD tan(17°).

Using the diagram,

x=BD-CD=AD tan(17°)-20sin(8°)

=(20cos(8°))tan(17°)-20sin(8°)

So everything is known and x can be calculated using a calculator.

I get x=5.9m.

## Answer This Question

## Related Questions

- trigonometric oblique triangle - a flagpole at a right angle to the hrizontal is...
- algebra - A flagpole at a right angle to the horizontal is located on a slope ...
- algebra 2 - A flagpole at a right angle to the horizontal is located on a slope ...
- 8 Grade Math - At the same time that a flagpole casts a 4.5 m shadow , a meter ...
- algebra 2 - Shalonda notices that when she stands next to the flagpole, she ...
- geometry - Shalonda notices that when she stands next to the flagpole, she casts...
- math/trig - A flagpole casts a shadow 44 ft with the sun angle of elevation is ...
- Math - A flagpole casts a shadow 30 feet long. A 5 foot woman standing next to ...
- Algebra - Ameter stick casts a shadow 1.4 m long at the same time a flagpole ...
- Math - The shadow of an object varies directly as its height h. A man 1.8 m tall...

More Related Questions