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Alina [70]
3 years ago
15

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 t

an 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.
Mathematics
2 answers:
almond37 [142]3 years ago
7 0
<span>a.
y = 15 tan(30°)
y = 15/√3 ≈ 8.66 ft
b.
y = 15 tan(40°) ≈ 12.59 ft
c.
A = 1/2 base x height ≈ 129.9 ft² and 188.8 ft² for 30° and 40°
hope it helps
</span>
Stella [2.4K]3 years ago
4 0

Answer:

A. 8.66 feet

B. 12.59 feet

C. Area of triangle when \theta=30  is 129.9 square feet. Area of triangle when \theta=40 is 188.85 square feet. Increasing the angle  \theta  increases the area.


Step-by-step explanation:

The equation that models the height of the triangle is:

y=15 Tan \theta

Where,

  • y is the height, and
  • \theta  is the angle

A.

When \theta=30 , the height is:

y=15Tan30\\y=8.66


B. When \theta=40[/tex\ , the height is:[tex]y=15Tan40\\y=12.59


C. <em>To find the area of the isosceles triangular shaped garden, we use the </em><em>formula for the area of the triangle</em><em>:</em>

A=\frac{1}{2}bh

Where,

  • A is the area
  • b is the base, which is given as 30 feet, and
  • h is the height [8.66 feet when the angle is 30 & 12.59 when angle is 40]

<u>When Vance uses \theta=30 , the area is</u>:

A=\frac{1}{2}(30)(8.66)\\A=129.9  square feet


<u>When Vance uses \theta=40 , the area is</u>:

A=\frac{1}{2}(30)(12.59)\\A=188.85  square feet


So we see that when the angle is more, the area is also more.

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