Quadrilateral QRST is inscribed in circle W as shown below. The measure of ∠QRS is 12 degrees less than three times the measure of ∠QTS and m RQT m RST ∠ = ∠ .

Arley is building a model of a city map. in one part of the city, three roads form a right triangle, which harley draws as triangle abc, with the following measures: m∠b=90° and m∠a=30°. in his scale model, the hypotenuse of triangle abc, ac¯¯¯¯¯¯¯¯, has a length of 817−−√ cm. what is the value of a (the length of bc¯¯¯¯¯¯¯¯)?

David is spreading mulch on a triangular area of his flower bed. the coordinates of the vertices of the area are (1, 3), (9, 3), and (4, 6). what is the area of the triangle if each square has an area of 3 square feet?

Awater tank holds 18000 gallons. how long will it take for the water level to reach 6000 gallons if the water is used at anaverage rate of 450 gallons per day