Angles
What is the general formula for all angles coterminal with 1000 degrees?
1000 +/- n (360); n = 0, 1, 2, 3,...
Given that sinθ > 0 and cosθ > 0, what quadrant will angle θ be in?
Quadrant 1
Write the Sine Law for a triangle ABC.
Sin A/ A = Sin B/ B = Sin C/ C
If we know the size of two sides of a triangle and the angle in between, we can use the cosine law to solve the triangle. True or false?
In a right triangle, if an angle θ is 20° and the side next to it is 12, what equation would be used to find the hypotenuse, x?
x = 12 cos 20
What quadrant is the angle 170 in?
Quadrant 2
Point P(3,-5) is on the terminal arm of an angle in standard position. What is the value of sinθ x cosθ ?
-15
For triangle DEF, d = 12 m, angle D = 23° and angle E = 112° . What is the size of e?
28.48 m
For triangle ABC, angle A = 75°, AC = 22 and AB = 15. What is the value of BC?
23.2.
In a right triangle, the side opposite an angle A is 24 cm. If tan A is 12/5, what is the size of the hypotenuse?
26
Draw the angle 213 in standard position.
Angle from positive x-axis.
What is tan 270 (without a calculator)?
No answer
For triangle ABC, if A = 35° , a = 22 cm and b = 36 cm. What are the values of angles B and C?
B = 69.81° , C = 75.19°
For triangle XYZ, x = 8 cm, y = 7 cm and z = 6 cm. What is the size of angle Z?
46.6°.
Solve the equation:
2 sin90 + cos180 - 5 tan360
1
What is the reference angle for 107° ?
73° .
Given that tanθ = 0.842, solve for θ to the nearest degree.
40 AND 220
For a triangle, given that a = 14 cm, angle A = 35° and angle B = 70° . Find the area of ABC.
155.31 cm2
A non-right triangle has sides 18, 20 and 24. Find the size of the LARGEST angle.
78.14°.
If I look at the top of a tower from point A, the angle of elevation is 43°. If I move 300 m forward to point B, the angle becomes 56°. What is the height of the tower?
754 m
An angle in the fourth quadrant has a reference angle of 14° . What is the value of the angle in standard position?
346°
If cosθ = -0.5, draw a diagram to show the angle(s) in standard position and the possible coordinates for point “P”.
θ = 120 or 240
P = (-0.5, √ 3/2) or (-0.5, -√ 3/2)
For triangle MNO, angle N = 62°, o = 31 m and n = 28 m. Solve the triangle and find all remaining sides and angles.
O = 77.83° , M = 40.17, m = 20.45 m
O = 102.16° , M = 15.84, m = 8.6 m
For triangle ABC, AC = 2x, BC = 2x+1 and angle C = 30°. If the area of ABC is 18, what is the value of x?
4
Two fire towers are 30 km apart. A fire is spotted from from the more distant West tower at 18° N of E, while the same fire is spotted from the East tower at 41° N of W. How much closer is the East Tower to the fire than the West Tower?
A. 9.7 km B. 12.1 km C. 10.8 km D. 12.7 km
B