Mathematics: 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 θ models the height of the triangular garden. what is the height of the triangle when θ = 30 ° ? what is the height of the triangle when θ = 40 ° ? vance is considering using either θ = 30 ° or θ = 40 ° for his garden. compare the areas of the two possible gardens. explain how you found the areas.

Yes u can :)) would be happy to help...

Vance is designing a garden in the shape of an isosceles

megan9246

10.03.2022

Part 1) The height of the triangle when θ = 30° is equal to $8.66\ ft$

Part 2) The height of the triangle when θ = 40° is equal to $12.59\ ft$

Part 3) The area of triangle with θ = 30° is less than the area of triangle with θ = 40°

Step-by-step explanation:

Part 1) What is the height of the triangle when θ = 30 ° ?

we have

$y=15tan(\theta)$

substitute the value of theta in the equation and find the height

$y=15tan(30\°)=8.66\ ft$

Part 2) What is the height of the triangle when θ = 40 ° ?

we have

$y=15tan(\theta)$

substitute the value of theta in the equation and find the height

$y=15tan(40\°)=12.59\ ft$

Part 2) Vance is considering using either θ = 30 ° or θ = 40 ° for his garden

Compare the areas of the two possible gardens

step 1

Find the area when θ = 30 °

The height is $8.66\ ft$

Remember that the area of a triangle is equal to the base multiplied by the height and divided by two

$A=(1/2)(30)(8.66)=129.9\ ft^{2}$

step 2

Find the area when θ = 40°

The height is $12.59\ ft$

Remember that the area of a triangle is equal to the base multiplied by the height and divided by two

$A=(1/2)(30)(12.59)=188.85\ ft^{2}$

Compare the areas of the two possible gardens

The area of triangle with θ = 30° is less than the area of triangle with θ = 40°

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