A triangular lot bounded by three streets has a length of 300 feet on one street, 200 feet on the second, and 120 feet on the third. The smallest angle formed by the streets is 30°. Find the area of the lot.
6,000 ft^2
9,000 ft^2
15,000 ft^2
30,000 ft^2

15,000 ft^2

Step-by-step explanation:

The triangle is not a right angle triangle. Therefore, the formula that would be used to determine the area of the triangle is expressed as

Area = 1/2abSinC

Where

a and b are the length of the sides of the triangle and C is the corresponding angle of side c

The given length of the sides of the triangle formed by the three streets are 300 feet, 200 feet and 120 feet.

If the smallest angle formed by the streets is 30°, then it corresponds to to the side whose length is 120 feet.

Therefore,

a = 300

b = 200

Angle C = 30°

Area = 1/2 × 300 × 200 × Sin30

Area = 15000 ft²

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: