1) A local naturalist says that a triangular area on the north side of a pond is a turtle habitat. The lengths of the sides of this area are 15 meters, 25 meters, and 36 meters. Which expression gives the measure of the angle between the sides of the habitat that measure 15 meters and 25 meters?
2) A statue is erected on a triangular marble base. The lengths of the sides of the triangle are 12 feet, 16 feet, and 18 feet. What is the area of the region at the base of the statue to the nearest square foot?
169 ft2
144 ft2
143 ft2
94 ft2
+23254 1) You have a triangle, call the angles A, B, and C, with opposite sides a, b, and c.
Let a = 15, b = 25, and c = 36. The angle between sides a and b is angle C.
Since you have SSS, use the Law of Cosines:
c² = a² + b² - 2·a·b·cosC
36² = 15² + 25² - 2·15·25·cosC
1296 = 225 + 625 - 750·cosC
1296 = 850 - 750·cosC
446 = -750·cosC
-0.594666 = cosC
angle C = 126.5 degrees
2) One formula for the area of a triangle is A = ½·a·b·sinC
Use the process of problem #1, to find the angle, then place the values into this equation.
+23254 1) You have a triangle, call the angles A, B, and C, with opposite sides a, b, and c.
Let a = 15, b = 25, and c = 36. The angle between sides a and b is angle C.
Since you have SSS, use the Law of Cosines:
c² = a² + b² - 2·a·b·cosC
36² = 15² + 25² - 2·15·25·cosC
1296 = 225 + 625 - 750·cosC
1296 = 850 - 750·cosC
446 = -750·cosC
-0.594666 = cosC
angle C = 126.5 degrees
2) One formula for the area of a triangle is A = ½·a·b·sinC
Use the process of problem #1, to find the angle, then place the values into this equation.
