Finding Sides
In triangle ABC, angle A = 40°, angle B = 60°, and side b = 12m. Find the length of side a.
a = 8.91m
When using the Sine Law to solve for an unknown angle θ, you isolate the term and get sinθ = 0.5. What is the measure of θ?
θ = 30°
Two observers look up at a drone. Observer A sees it at an angle of elevation of 40°. Observer B sees it at 50°. If the observers are standing on opposite sides of the drone, what is the third angle inside the triangle formed by the drone and the two observers?
90°
In triangle ABC, angle A = 40°, angle B = 60°, and side b = 12 cm. Set up the Sine Law proportion you would use to find the length of side a.
a/sin40° = 12/sin60°
When using the Sine Law to solve for an unknown acute angle θ, you isolate the term and get sinθ = 0.25. What is the measure of θ to the nearest degree?
14°
In triangle DEF, angle D = 72°, angle E = 48°, and side e = 15cm. What is the measure of side d?
d = 19.2 cm
In triangle ABC, side a = 8 c, side b = 11 cm, and angle B = 65. Set up the Sine Law equation to solve for angle A.
sinA/8 = sin65°/11
A surveyor stands between two towers. The distance from the surveyor to Tower 1 is 50 m. The angle between the ground lines to the tops of the towers from the surveyor is 60°. If the angle at Tower 2 is 45°, how far is the surveyor from Tower 2? (Assume a flat triangular path).
61.2 m
In triangle DEF, angle D = 72°, angle E = 48°, and side f = 15 cm. What is the measure of the third angle, angle F
F = 60°
In triangle ABC, side a = 8 cm, side b = 11 cm, and angle B = 65°. Set up the Sine Law equation to solve for the acute angle A.
sinA/8 = sin(65°)/11
In triangle PQR, angle P = 35°, angle Q = 85°, and side q = 22 cm. Calculate the length of side p to the nearest tenth.
p = 12.7 cm
In triangle LMN, side l = 14 cm, side m = 19 cm, and angle M = 74°. Find the measure of angle L to the nearest degree.
L = 45°
A leaning flagpole tilts forward toward the sun at an angle of 95° from the ground. It casts a shadow that is 8.2 m long. The angle of elevation from the tip of the shadow to the top of the flagpole is 38°. How tall is the flagpole to the nearest tenth of a meter?
7.1 m
In triangle XYZ, angle X = 78°, angle Y = 32°, and side x = 28.5 cm. Calculate the length of side z to the nearest tenth.
z = 29.7 cm
In triangle RST, side r = 12.5 m, side s = 9.2 m, and angle R = 42°. Find the measure of angle S to the nearest degree
S = 30°
Two points, A and B, are on opposite sides of a river. A surveyor shifts 100 m along the bank from point A to a new point C. angle BAC is measured to be 72° and angle BCA is 58°. Calculate the width of the river (the direct distance from A to B) to the nearest meter.
111 m
In triangle XYZ, angle X = 65°, angle Y = 45°, and side x = 18.5 cm. Calculate the length of side z to the nearest tenth.
z = 19.1 cm
In triangle RST, side r = 13.2 m, side s = 9.5 m, and angle R = 58°. Find the measure of angle S to the nearest degree
S = 38°
An isosceles triangle has a base of 10. The two equal angles at the base each measure 55. Use the Sine Law to find the length of one of the equal sides to the nearest tenth.
8.7 cm
In acute triangle ABC, side a = 7.8 cm, side c = 9.2 cm, and angle C = 70°. Solve for the measure of the remaining acute angle, B, to the nearest whole degree.
B = 57°
Two boats leave a dock at the same time traveling in different directions. The angle between their paths is 64°. After one hour, Boat A is 25 km away from the dock. The distance directly between the two boats at this time is 32 km. Find the distance from the dock to Boat B to the nearest kilometer.
34 km
An isosceles triangle has a base of 10 cm. The two equal angles at the base each measure 55°. Use the Sine Law to find the length of one of the equal sides to the nearest tenth.
8.7 cm
In triangle ABC, a = 9.0 cm, c = 11.5 cm, and angle C = 72°. Find the measure of the remaining acute angle, B, to the nearest degree.
B = 60°