The Law of Sines
The Law of Sines is a relationship between the _________ and __________ in oblique triangles.
sides, angles
The area of a triangle equals ________ the product of the lengths of two sides times the ______ of their included angle.
one-half, sine
The Law of Cosines is used to solve triangles which ____ sides and the included angle (SAS) are known, or those in which _____ sides (SSS) are known.
2, 3
(SAS TRIANGLE (LAW OF COSINES)) Solve the triangle ABC when A= 60 degrees, b=30, and c=30 (round to the nearest tenth for side lengths and round to the nearest degree for angle measures).
a= (about 26.5) B=(about) 41 degrees C=(about) 79 degrees
What is the S part of Heron's Formula for the Area of a Triangle, s=......
What are the 3 ratios used in the Law of Sines?
a/sinA, b/sinB, c/sinC
What are the 3 formulas for the area of an oblique triangle?
Area= 1/2 bc sin A, 1/2 ab sin C, 1/2 ac sin B
In the Law of Cosines, the _______ of a side of a triangle equals the sum of the squares of the other ____ sides minus twice their product times the cosine of their included angle.
square, 2
(SSS TRIANGLE (LAW OF COSINES)) Solve for triangle ABC when a=10, b=12, and c=16 (Round to nearest degree).
A= (about) 39 degrees B= (about) 48 degrees C=(about) 93 degrees
What is the formula for area using Heron's Formula; Area=.......
Area= √s(s-a)(s-b)(s-c) (the square root is over everything)
The Law of Sines can be used to solve a triangle in which ___ side and ___ angles are known, (but one of the ratios must be there or solved for). hint ASA and SAA
1, 2
What is the area of triangle ABC that uses, b= 20 ft, c=40 ft, A=48 degrees (Round to the nearest square foot)
Area =(about) 297 square feet
What is one example of the formula for the Law of Cosines?
a2=b2+c2 - 2bc cos A
b2=a2+c2 - 2ac cos B
c2=a2+b2 - 2ac cos C
(SSA Triangle (LAW OF SINES)) Solve for triangle FGH when F= 40 degrees g=8 f=10 (Round angle to the nearest angle and round the side length to the nearest tenth).
G= (about) 31 degrees H= (about) 109 degrees h= (about) 14.7
Find the area of triangle ABC when a= 13 yards, b= 9 yards, and c= 5 yards (round to the nearest square unit)
Area= (about) 16 square yards
Solve for side c in triangle ABC using the Law of Sines using b=7 B=35 degrees C=105 degrees (round to the nearest tenth).
c= (about) 11.8
What is the area of the triangle ABC, when A=62 degrees, b=10 feet, and c=24 feet. (Round to the nearest square foot)
The area of the triangle ABC is about 106 square feet.
Solve for c of triangle ABC when C= 37 degrees, b=11 a=8 (round to the nearest tenth)
c= (about) 6.7
(SAS TRIANGLE (LAW OF COSINES)) Solve for triangle ABC when a=6, b=4, and C=96 degrees (Round lengths of sides to the nearest tenth and angle measures to the nearest degree).
c= (about)= 7.6 B= (about) 32 degrees C=(about) 52 degrees
Find the area of triangle ABC when a= 16 meters, b= 10 meters, and c= 8 meters (round to the nearest square unit).
Area =(about) 33 square meters.
Solve triangle ABC using the law of sines A=50 degrees, C=33.5, and b=76 (hint: first solve for B and then make a ratio)
B= 96.5, a=(about) 58.6 and C = (about) 42.2
What is the area of the triangle ABC, when C= 102 degrees, a=16 feet, and b=20 feet. (Round to the nearest square foot)
Area= (about) 157 square feet
Solve for z of triangle XYZ when Z= 131 degrees, y=6.5, x=9.4 (round to the nearest tenth)
z= (about) 14.5
(SSS TRIANGLE (LAW OF COSINES)) Solve triangle ABC when a=6, b=4, and c=3 (Round angle measures to the nearest degree).
A= (about) 117 degrees B= (about) 37 degrees C= (about) 26 degrees
Find the area of triangle ABC when a= 5 feet, b= 5 feet, and c= 4 feet (round to the nearest square unit)
Area = (about) 9 square feet