Equations to Know
Right Triangle Trig (8.1)
Law of Sines (8.2)
Law of Cosines (8.3)
Area of a Triangle (8.4)
100
Given right triangle ABC, what are the two "formulas" you need to remember to solve the triangle?
1. SOH CAH TOA
2. a2 + b2 = c2
100
What is the value of sin Ѳ ? (Remember to rationalize the denominator.)
sqrt6/3
100
Solve for angle C, side a, and side b. Round decimals to 4 places.
angleC = 95^o
a ~~ 2.8392 units
b ~~ 2.5810 units
100
In triangle ABC, b = 1, c = 3, and the measure of angle A is 80o. What is the length of side a? Round decimals to 4 places.
2.9930 units
100
What is the area of the triangle above? Round decimals to 4 places.
2.9886 units2
200
Given triangle ABC, what is the entire equation for the Law of Sines?
Sin A/a = Sin B/b = Sin C/c
200
Find the exact value of:
cot 40^o - sin 50^o/sin 40^o
0
200
In triangle ABC, a = 4, b = 5, angle A = 60o .
1. How many possible different triangles exist for ABC?
2. If triangle/s exist, what is the measure of angle B? Round decimals to 4 places.
No triangles exist
200
Solve for the measure of angle A. Round decimals to 4 places.
mangleA ~~ 125.0996^o
200
In triangle XYZ, x = 5, y = 8, and z = 9. What is the area of the triangle? Round decimals to 4 places.
19.8997 units2
300
Given triangle ABC, what are the three equations for the Law of Cosines?
a^2 = b^2 + c^2 - 2bc(cosA)
b^2 = a^2 + c^2 - 2ac(cosB)
c^2 = a^2 + b^2 - 2ab(cosC)
300
A right triangle has a hypotenuse of length 8 inches. If one angle is 35o, find the length of each leg. Round decimals to 4 places.
4.5886 inches and 6.5532 inches
300
In triangle ABC, b = 4, c = 5, angle B = 40o .
1. How many possible different triangles exist for ABC?
2. If triangle/s exist, what is the measure of angle C? Round decimals to 4 places.
angleC~~ 53.4641^o or 126.5359^o
300
Two ships are sailing from Seattle. The Nina is sailing due west and the Pinta is sailing 43o due south of west. After an hour, the Nina has sailed 115 km and the Pinta has sailed 98 km. How far apart are the two ships? Round decimals to 4 places.
79.6510 km
300
A surveyor measures a triangular plot of land that measures 203.5 ft by 189.1 ft by 264.8 ft. What is the area of the plot? Round decimals to 4 places.
19,159.9846 ft2
400
Suppose you were given the measure of angle C and the side lengths of a and b in the triangle above, which equation would you use to solve for the area of the triangle?
K = 1/2 ab Sin C
400
A security camera outside of a building is mounted on a wall 12 feet above the ground. What angle of depression should be used if the camera is to be directed to a spot 8 feet above the ground and 10 feet from the wall? Round decimals to 4 places.
21.8014o
400
At exactly the same time, Tom and Alice measured the angle of elevation to the moon while standing exactly 300 km apart. Tom measured 49.8974o, while Alice measured 49.9312o. How far was the moon from Earth at that time? Round decimals to 4 places.
297,675.6249 km
400
Alvin, Simon, and Theodore are camping in their tents. If the distance between Alvin and Simon is 153 feet, the distance between Alvin and Theodore is 201 feet, and the distance between Simon and Theodore is 175 feet, what is the angle between Simon, Theodore, and Alvin? Round decimals to 4 places.
47.4014o
400
Find the area of the shaded region in the figure above. Triangle PQR is a right triangle. Round decimals to 4 places.
15.2699 units2
500
Suppose you were given the measures of the sides a, b, and c in the triangle above, which equations would you use to find the area of the triangle?
s =1/2(a + b + c)
K=sqrt(s(s - a)(s - b)(s - c)
500
The Freedom Tower in NYC is 1776 feet tall (without the antenna). The angle of elevation from an office building is 34o. The angle of elevation from the helipad on the roof of the office building to the top of the tower is 20o. How tall is the office building? Round decimals to 4 places.
817.6561 feet
500
A forest ranger is walking along a path inclined at 5o to the horizontal directly toward a 100-foot-tall fire tower. The angle of elevation from the path to the top of the fire tower is 40o. How far is the ranger from the tower at this time? Round decimals to 4 places.
110.0063 feet
500
A radio tower 500 ft high is located on the side of a hill with an inclination to the horizontal of 5o. How long should two guy wires be if they are to connect to the top of the tower and be secured at two points 100 directly above and directly below the base of the tower? Round decimals to 4 places.
518.3778 ft and 501.2828 ft
500
What is the area of the quadrilateral above? Round decimals to 4 places.
76.4498 cm2