Question

Help!! I'll give you a metal!

Vance is designing a garden in the shape of an isosceles triangle. The base of the garden is 30 feet long. The function y = 15 tan theta models the height of the triangular garden.

a. What is the height of the triangle when theta = 30°?

b. What is the height of the triangle when theta = 40°?

c. Vance is considering using either theta = 30° or theta = 40° for his garden. Compare the areas of the two possible gardens. Explain how you found the areas.

Answer 1

For a, plug in 30 to theta, which should give you this: (make sure your calculator is in degrees)
\[y = 15\tan (30) = 8.66025 \approx 8.660 ft\]
and do the same for b, plugging in 40.

Answer 2

Then use the formula for area of a triangle (A=.5bh) with each answer, where b = 30 ft and \[h = 15\tan(\theta)\]

Answer 3

thanks!!!

Answer 4

Glad it helped. :)

Answer 5

can you help a little more on c im kinda stuck?

Answer 6

Yes, where are you stuck?

Answer 7

im stuck on figuring out to to begin working it out. i dont really understand the question

Answer 8

Well it is asking you to find the two areas of triangles where theta is 40 degrees and 30 degrees. So first you must find their areas.
The area of a triangle is given by \[A = \frac{ 1 }{ 2 }(b)(h)\] where b is the base of the triangle and h is the height of the triangle. The base is given to you in the question: 30 feet. And h will be your answers for a and b.
After you have the two areas, all it's asking is that you state which is larger, and the "explain" portion of the question will simply be what you've already worked out by finding the areas.

Answer 9

okay i'll try thanks!!!