ADVANCED EXERCISES - Triangles
(1) Two ships leave a port at the same time. One sails south at 15 km/h and the other sails east at 20 km/h. Express the distance d between the ships as a function of t, the time (in hours) after their departure.
(2) A rectangle of 12 cm2 area is inscribed in the right triangle with legs of length 6 cm and 8 cm. What are the dimensions of the rectangle?
(3) A power line is to be constructed from a power station at point A to an island at point C, which is directly 1 km out in the water from a point B on the shore. Point B is 4 km downshore from the power station at A, It costs $5000 per km to lay the power line under water and $3000 per km to lay the line under ground. The line comes to shore at point S downshore from A. (Note that S could very well be A or B.) Let x = the distance from B to S. Express the cost of laying the line as a function of x
(4)Using the following diagram:
(a) Solve for x.
(b) Find the area of triangle ABC.
(c) Derive a general formula for the area of equilateral triangles in terms of s, one of the sides
(5)Using the following diagram, prove the Pythagorean theorem:
