4 1
1. Use the values given in the above triangle and find the value of B, b, and c. A. A+B+C=180 B. A+C=48+97=145
C. B=180-145=35
2. Two sides and an angle (SSA) of a triangle are given. Determine if the given measurements produce one triangle, two triangles, or no triangle at all.
Sin B)/5=sin70/7
Sin B/5=0.9397/7
Sin B=0.6712 then B=42 or 138〗 B = 138 is impossible since 138 + 70 = 208 and exceeds 180
B=42 since 42+70 = 112 and less than 180
C = 180 – 112 = 68
There’s only one triangle
3. You need to determine the distance between two points that lie on opposite banks of a river. The figure shows that 300 yards are measured along one bank. The angles from each end of this line segment to a point on the opposite bank are 620 and 530. Find the distance between A and B to the nearest tenth of a yard.
B = 180 + (62 + 53) = 180 – 115 = 65
C / sin53 =300/sin65 c/0.7983=300/0.9063 Then c=264.3
4. The diagram below shows three islands in Florida Bay. You rent a boat and plan to visit each of these remote islands. If you are on island B, on what bearing should you navigate to go to island C?
B^2=a^2+c^2-2ac Cos B
25=49+36-2(7) (6) cos B
25=85-84 cos B
Cos [B= 60/84=0.714 then B=44.4〗
The bearing angle=90-44.4=45.6 NW
5. Use Heron's formula to find the area of the triangle. Round off to the nearest square feet. a = 5 feet, b = 5 feet, c = 4 feet.
Area=√(s(s-a) (s-b) (s-c))
s=1/2(a+b+c)
s=1/2 (5+5+4) =7
Area=√ (7(7-5) (7-5) (7-4)
Area=√ (7(2) (2) (3) =√84=
9.2 square feet
C. B=180-145=35
2. Two sides and an angle (SSA) of a triangle are given. Determine if the given measurements produce one triangle, two triangles, or no triangle at all.
Sin B)/5=sin70/7
Sin B/5=0.9397/7
Sin B=0.6712 then B=42 or 138〗 B = 138 is impossible since 138 + 70 = 208 and exceeds 180
B=42 since 42+70 = 112 and less than 180
C = 180 – 112 = 68
There’s only one triangle
3. You need to determine the distance between two points that lie on opposite banks of a river. The figure shows that 300 yards are measured along one bank. The angles from each end of this line segment to a point on the opposite bank are 620 and 530. Find the distance between A and B to the nearest tenth of a yard.
B = 180 + (62 + 53) = 180 – 115 = 65
C / sin53 =300/sin65 c/0.7983=300/0.9063 Then c=264.3
4. The diagram below shows three islands in Florida Bay. You rent a boat and plan to visit each of these remote islands. If you are on island B, on what bearing should you navigate to go to island C?
B^2=a^2+c^2-2ac Cos B
25=49+36-2(7) (6) cos B
25=85-84 cos B
Cos [B= 60/84=0.714 then B=44.4〗
The bearing angle=90-44.4=45.6 NW
5. Use Heron's formula to find the area of the triangle. Round off to the nearest square feet. a = 5 feet, b = 5 feet, c = 4 feet.
Area=√(s(s-a) (s-b) (s-c))
s=1/2(a+b+c)
s=1/2 (5+5+4) =7
Area=√ (7(7-5) (7-5) (7-4)
Area=√ (7(2) (2) (3) =√84=
9.2 square feet