Question

3.5 m Two sides of a triangle have length 2.5 meters and 3.5 meters, and the angle formed by these two sides has a mea- sure of 60°. Determine the area of the triangle. Note: This is the triangle in Progress Check 3.17 on page 200. 60° B 2.5 m A field has the shape of a quadrilateral that is not a parallelogram. As shown in the following diagram, three sides measure 50 yards, 60 yards, and 70 yards. Due to some wetland along the fourth side, the length of the fourth side could not be measured directly. The two angles shown in the diagram measure 127° and 132º. 60 yards 132 70 yards 127° 50 yards wetland Determine the length of the fourth side of the quadrilateral, the measures of the other two angles in the quadrilateral, and the area of the quadrilateral. Lengths must be accurate to the nearest hundredth of a yard, angle measures must be correct to the nearest hundredth of a degree, and the area must be correct to the nearest hundredth of a square yard.

Answer 1

solutions А from cosine Rule 2 3.5m С &= a +5-rab copt B 60 B 2.5m ² = 2.5² +3.5 & 2 (2.5) (3.5) cos(60) c = 9.75 "c=3.122 Som sine Rule Sinc SinA= 2.5 sin60° Sin A 2.5 3.122 3.122 Sin A=0.693375 d :) Aa 43.891 60 -43. 897. B = 180 B= 72.8102