MODERATE EXERCISES - Triangles
(1) The length of a side of an equilateral triangle is 80 cm.
(a) Find the height of the triangle.
(b) Find the area of the triangle.
(c) If the triangle were being constructed out of fabric costing $2 per square meter, how much would it cost to make the triangle?
(2) Express the area of an equilateral triangle as a function of the length x of a side.
(3) A boardwalk is parallel to and 210 feet inland from a straight shore line. There is a sandy beach between the boardwalk and the shore line. A man is standing on the boardwalk, exactly 750 feet across the sand from his beach umbrella, which is right at the water-line. The man walks 4 feet/sec on the boardwalk and 2 feet/sec on the sand. How far should he go on the boardwalk before veering off into the sand if he wishes to reach his umbrella in exactly 4 minutes and 45 seconds?
(4) An isosceles triangle has a perimeter of 42 cm. Express the area A of the triangle as a function of the length b of the base of the triangle.
(5) An airplane is flying at an altitude of 3700 ft. The distance directly to the airport is d ft. (This distance is at an angle to the horizontal.) Express the horizontal distance h as a function of d.
(6) A girl is at point A on a bank of a straight river which is two miles wide. She wants to reach point B, which is across the river and 7 miles downstream, by first rowing her boat to a point P on the opposite bank and then walking the remaining distance, x, to B. She can row at 4 miles/hour and walk at 3 miles/hour. Express the total time T that she takes to go from A to B as a function of x.
(a) Given the diagram (note that triangle ABC is equilateral), calculate the length of altitude BD
(b) From triangle BDC (which is a 30:60:90 triangle), what general ratio (hypotenuse:short leg:long leg) can be seen?
