Sines
If A = 63, B = 19, and a = 2.4, find b to the nearest tenth, using Law of Sines.
0.9
If a = 21.5, b = 13, and C = 39, find c to the nearest tenth, using the Law of Cosines.
14.1
Find the area of triangle ABC if a = 15, b = 20, and c = 25, to the nearest whole number.
150
From a point 80 m from the base of a tower, the angle of elevation to the top of the tower is 28 degrees. How tall is the tower, to the nearest tenth?
42.5 meters
A triangle has side lengths 6, 11, and 16. Classify the triangle by side angles and side lengths.
Obtuse Scalene Triangle
If B = 14, C = 45, and b = 5.2, find c to the nearest tenth, using Law of Sines.
15.2
If A = 52, b = 54, and c = 49, find a to the nearest tenth, using the Law of Cosines.
45.3
Find the area of triangle ABC if a = 3, b = 19, and c = 21, to the nearest tenth.
22.3
A wire is attached to the top of a tower and a point on the ground that is 35 m away from the base of the tower. If the wire is 127 m long, what angle does the wire make with the ground? Round to the nearest whole number.
74 meters
Find the geometric mean between 36 and 25.
30
If a = 12, B = 27, and b = 15, find A to the nearest degree, using the Law of Sines.
21
If a = 3, b = 7, and c = 5, find B to the nearest whole number, using the Law of Cosines.
120
Find the area of triangle ABC if B = 25, a = 17, and c = 33, to the nearest whole number.
119
An observer on a cliff 100 ft above sea level sees two ships in the distance. The angles of depression of the ships are 47 and 32. Find, to the nearest hundreth, the distance between the two ships.
66.75 feet
An equilateral triangle has a perimeter of 30 inches. Find its height. Your answer should be a radical in simplest form.
5√ 3
If A = 50, b = 10, and a = 14, find C to the nearest degree, using the Law of Sines.
97
If a = 5, b = 6, and c = 8, find A to the nearest whole number, using the Law of Cosines.
39
Find the area of triangle ABC if A = 32, b = 10, and c = 12, to the nearest tenth.
31.8
The cities of Algebra, Geometry, and Trigonometry are connected by 3 roads on a map. The road from Algebra to Geometry is 17 miles long. The angle between the roads from Algebra to Geometry and Trigonometry is 61 degrees. The angle formed by the roads from Trigonometry to Algebra and Geometry is 48 degrees. How long is the road from Trigonometry to Geometry, to the nearest whole number?
20 miles
Name 4 different Pythagorean Triples (no multiples).
3, 4, 5
5, 12, 13
7, 24, 25
8, 15, 17
9, 40, 41
20, 21, 29
If A = 123.9, B = 22.2, and b = 27.5, find c to the nearest tenth, using the Law of Sines.
40.6
If a = 12.6, b = 8.5, and c = 6.3, find C to the nearest tenth, using the Law of Cosines.
26.7
Find the area of triangle ABC if A = 36, b = 4, and c = 7, to the nearest tenth.
8.2
Scientists in Houston are trying to figure out the distance from a satellite to Cape Canaveral. They know that the satellite is 530 miles from Houston at an 85º angle of elevation, and Houston and Cape Canaveral, in a straight line from one to the other, are 902 miles apart. How far is the satellite from Cape Canaveral? (nearest hundreth)
1005.57 miles
When was Trigonometry first formally documented? (answer must be within 100 years)
150 BCE
(Hipparchus, ancient Greece)