Question

a triangular plot of land is enclosed by a fence. two sides of the fence are 9.8 m and 6.6 m long, respectively. the other side forms an angle of with the 9.8 m side. a) draw a sketch of the situation. b) calculate the height of the triangle to the nearest tenth. compare it to the given sides. c) how many lengths are possible for the third side? explain.

Answer 1

The height of the triangle cannot be determined without more information, such as the angle or length of the third side. However, the possible length of the third side ranges from 3.2 m to 16.4 m, based on the triangle inequality theorem.

Step-by-step explanation:

A student wants to calculate the height of a triangular plot of land with sides 9.8 m and 6.6 m long. Without additional information, such as the angle between the sides or the length of the third side, we cannot determine the height. We could determine possible lengths for the third side using the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the length of the third side.

The many possible configurations of the third side depend on the angle it makes with the known sides. Given the lengths of the two sides (9.8 m and 6.6 m), the possible length of the third side could be any value between the difference and the sum of these two lengths (3.2 m to 16.4 m) because a triangle cannot have a side with a negative length and a side cannot be longer than the sum of the other two sides.