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.

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

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

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

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

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

we have

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

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

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

so

step 2

Find the area when θ = 40°

The height is

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

so

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°

answer: given that the roller coaster can accommodate 1600 riders per hour, thus the roller coaster can accomodate 1600 / 60 = 26.67 riders per minute.

given that there are 345 people in the line, the number of minutes it will take for the 345 persons to get into the roller coaster is given by 345 / 26.67 = 12.94 minutes.

therefore, it will take you 12.94 minutes to get to the front of the line.

step-by-step explanation:

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step-by-step explanation: