word problem

[lageda]

Height of a post. Betty observed that the lamp post in
front of her house casts a shadow of length 8 feet when
the angle of inclination of the sun is 60 degrees. How tall
is the lamp post? (In a 30-60-90 right triangle, the side
opposite 30 is one-half the length of the hypotenuse.)

 

[mmm4444bot]

Do you understand how to draw a right triangle, from the given information? The pole and the shadow are the legs of the right triangle.

Have you learned how to use the Pythagorean Theorem, yet?

Where are you stuck?

 

[lageda]

The entire problem confuses me I'm not even sure how to set up the problem

 

[mmm4444bot]

Hold on; I'm drawing a picture.

 

[mmm4444bot]

The given senario generates a 30-60-90-degree right triangle.

[attachment=0:1ht54iec]shadow.jpg[/attachment:1ht54iec]

The "hypotenuse" is the longest side.

What does the exercise say about the relationship between the hypotenuse and the side opposite the 30-degree angle ?

 

[lageda]

the side opposite of 30 is half of the length of the hypotenuce so does that mean its 4ft insteasd of 8 or would the final answer be half???

 

[mmm4444bot]

To say that something is half of another means the other is twice as much.

If you're half my age, then I'm twice your age.

If my car costs half as much as yours, then your car is twice the cost of mine.

If the shadow is half as long as the hypotenuse, then the hypotenuse is twice the shadow.

Therefore, the hypotenuse is twice 8 ft.

Now we know the lengths of two sides of this 30-60-90-degree triangle.

(1) The base: 8

(2) The hypotenuse: 16

The Pythagorean Theorem relates the three sides of any right triangle.

The sum of the squares of the legs equals the square of the hypotenuse.

(3) Let the symbol h represent the height of the pole.

h^2 + (8)^2 = (16)^2

Does this ring any bells?

 

[lageda]

ok I think I got it thanks

 

[BigGlenntheHeavy]

\(\displaystyle h \ (height \ of \ pole) \ = \ 8tan(60^0).\)