Trigonometry
Improve your experience by picking them
Identify whether the following measurements of two sides and an angle can produce one triangle, two triangles, or no triangle. Find the missing side lengths and angles of the triangle. Express the lengths and angles in one decimal place.
a = 35, b = 28, A = 70°
a = 45.3, c = 37.6, A = 128°
a = 5.3, b = 3, A = 155°
a = 15, b = 45, A = 148°
a = 35, b = 50, A = 25°
a = 12, b = 35, A = 18°
a = 86, c = 116, A = 43°
a = 1.8, b = 3.7, A = 131°
Find the missing side length and angles of the triangle. Express the length and angles in one decimal place.
q = 450, p = 250
C = 70°, a = 4, c = 2
B = 32°, a = 15.7, b = 11.2
Complete the following statement.
A triangle that has two equal sides is known as a/an ___.
Identify whether the following information is sufficient to solve the triangle with the help of the law of sines.
Three angles are given.
Find the missing side lengths and angle of the triangle ABC.
A=47.82°,B=72.34°,a=11.21 ftA=47.82\degree,B=72.34\degree,a=11.21\text{ ft}A=47.82°,B=72.34°,a=11.21 ft
B=41°30′,a=23.5 cm,C=97°20′B=41\degree30^{\prime},a=23.5\text{ cm},C=97\degree20^{\prime}B=41°30′,a=23.5 cm,C=97°20′
A=31.65°,C=26.21°,b=49.24 mA=31.65\degree,C=26.21\degree,b=49.24\text{ m}A=31.65°,C=26.21°,b=49.24 m
B=38.77°,C=109.45°,b=4726 ftB=38.77\degree,C=109.45\degree,b=4726\text{ ft}B=38.77°,C=109.45°,b=4726 ft
C=69°28′,c=31.92 mm,A=36°49′C=69\degree28^{\prime},c=31.92\text{ mm},A=36\degree49^{\prime}C=69°28′,c=31.92 mm,A=36°49′
A group of students in Bangkok, Thailand, is performing an activity in the vicinity of the Chao Phraya River. The measurements (angles and length) they obtained are shown in the figure. Determine the distance DE that runs across the river.
The geologists from Geo Experts Co. are conducting fieldwork at a valley. Their measurements are shown in the figure. Determine the distance TU.
A jet ski is heading north. At one moment, the bearing of a buoy 872 m away is N 53.1° E. After some time, the bearing of the buoy was observed as S 37.2° E. Determine the distance that the jet ski has traveled between the times that the bearing of the buoy was measured.
Two telecommunication towers, K, and L, are situated on a north-south line, with K located to the north of L. The distance between the telecommunication towers is 8.34 mi. From K, the bearing of a power transmission tower is 126.3°, and from L, the bearing is 73.8°. Determine the distance between K and the power transmission tower.
A car is traveling on a road that stretches along a north-south line. The bearing of a windmill from the car was measured N 48° E. After traveling 5.2 mi towards the north, another bearing was taken as N 64° E. Calculate the distance between the car and the windmill at the time when the first bearing was measured.
Dave and Jane are standing on the same side of the street sidewalk as they wait for their school bus. Dave spotted a traffic cone on the opposite sidewalk and observed its bearing as 27.85°. Jane is 7.4 m away from Dave and saw the traffic cone at a bearing of 351.46°. Calculate the width of the street.
Find the missing side length of the triangle ABC.
Determine the area of a triangle ABC with the following measurements.
A=48.5°,b=17.8 m,c=29.3 mA=48.5\degree,b=17.8\text{ m},c=29.3\text{ m}A=48.5°,b=17.8 m,c=29.3 m
B=136.8°,a=35.8 cm,c=22.6 cmB=136.8\degree,a=35.8\text{ cm},c=22.6\text{ cm}B=136.8°,a=35.8 cm,c=22.6 cm
A=67.50°,b=43.58 ft,c=59.62 ftA=67.50\degree,b=43.58\text{ ft},c=59.62\text{ ft}A=67.50°,b=43.58 ft,c=59.62 ft
A=62.34°,b=23.00 cm,C=42.87°A=62.34\degree,b=23.00\text{ cm},C=42.87\degreeA=62.34°,b=23.00 cm,C=42.87°
Find the number of possible triangles with the following measurements.
a=47,b=19,A=115°a = 47, b = 19, A = 115°a=47,b=19,A=115°
a=52,b=46,B=59°a = 52, b = 46, B = 59°a=52,b=46,B=59°
c=70,b=83,C=79°c = 70, b = 83, C = 79°c=70,b=83,C=79°
Determine the measure of angle B in the given figure.
Determine the measure of the remaining angles of a triangle ABC with the following measurements.
A=22.9°,b=49.2 ft,a=23.7 ftA=22.9\degree,b=49.2\text{ ft},a=23.7\text{ ft}A=22.9°,b=49.2 ft,a=23.7 ft
C=32°35′,b=17.8 m,c=25.6 mC=32\degree35^{\prime},b=17.8\text{ m},c=25.6\text{ m}C=32°35′,b=17.8 m,c=25.6 m
B=81.8°,a=897 m,b=824 mB=81.8\degree,a=897\text{ m},b=824\text{ m}B=81.8°,a=897 m,b=824 m
A=151.69°,b=8.796 ft,a=10.654 ftA=151.69\degree,b=8.796\text{ ft},a=10.654\text{ ft}A=151.69°,b=8.796 ft,a=10.654 ft
Determine the length of a line drawn from the point to the positive x-axis such that two triangles are possible.
Determine the length of a line drawn from the point to the positive x-axis such that only one triangle is possible.
Determine the length of a line drawn from the point to the positive x-axis such that no triangle is possible.
Choose the measurements that will not result in a unique triangle.
Dianne is going to cut cartons into triangular shapes, which will be used as decorations for a birthday party. Two sides of the triangle have lengths of 12.3 cm12.3~\text{cm}12.3 cm and 15.7 cm15.7~\text{cm}15.7 cm. If the angle between these sides is 98∘98^{\circ}98∘, what is the area of each triangular carton?
A triangular swimming pool will be constructed in a hotel. Two sides of the pool measure 10.5 m10.5~\text{m}10.5 m and 12.6 m12.6~\text{m}12.6 m. The angle between these sides is 58.1∘58.1^\circ58.1∘. What is the area of the swimming pool?
The given set of measurements describes triangle ABCABCABC. Use the law of sines to find bbb.
C=68.1∘,c=27.4 cm,B=32.2∘C=68.1^\circ,c=27.4~\text{cm},B=32.2^\circC=68.1∘,c=27.4 cm,B=32.2∘
The given set of measurements describes triangle ABCABCABC. Use the law of sines to find BBB.
C=62.9∘,c=45.7 ft,b=33.3 ftC= 62.9^\circ,c=45.7~\text{ft},b=33.3~\text{ft}C=62.9∘,c=45.7 ft,b=33.3 ft
a=394 m,A=108.8∘,B=43.1∘a=394~\text{m},A=108.8^\circ,B=43.1^\circa=394 m,A=108.8∘,B=43.1∘
A=49.12°,a=27.8 m,b=21.75 mA=49.12\degree,a=27.8\text{ m},b=21.75\text{ m}A=49.12°,a=27.8 m,b=21.75 m
B=61.1°,b=99.8 m,c=183 mB=61.1\degree,b=99.8\text{ m},c=183\text{ m}B=61.1°,b=99.8 m,c=183 m
A=45°38′,a=14.58 m,b=13.47 mA=45\degree38^{\prime},a=14.58\text{ m},b=13.47\text{ m}A=45°38′,a=14.58 m,b=13.47 m
A=107.52°,b=5.327 ft,a=8.965 ftA=107.52\degree,b=5.327\text{ ft},a=8.965\text{ ft}A=107.52°,b=5.327 ft,a=8.965 ft
B=57.43°,a=65.29 cm,b=79.86 cmB=57.43\degree,a=65.29\text{ cm},b=79.86\text{ cm}B=57.43°,a=65.29 cm,b=79.86 cm
Ben is fascinated with the beauty of Kyoto, Japan, as he gazes out of the observation deck at Kyoto Tower. He finds that the angle of depression of a cherry blossom tree is 63°, and a nearby restaurant is at an angle of depression of 70°. The cherry blossom tree, Kyoto Tower, and the restaurant are collinear. If the distance between the tree and the restaurant is 88 m, how high is the observation deck relative to the ground?
Determine the measure of angle C in the triangle ABC. Also, identify the type of the triangle.
a=67,c=127,A=30°a=6\sqrt7,c=12\sqrt7,A=30\degreea=67,c=127,A=30°
Without using the law of sines, choose the correct reason for the non-existence of the triangle with the following measurement.
A=117°40′,a=27.9 cm,b=36.2 cmA=117\degree40^{\prime},a=27.9\text{ cm},b=36.2\text{ cm}A=117°40′,a=27.9 cm,b=36.2 cm
Determine the measure of angle B in the triangle ABC. Use the calculator.
A=119°,a=37.2,b=48.5A = 119°, a = 37.2, b = 48.5A=119°,a=37.2,b=48.5
Determine whether the given statement is true or false.
a+ba−b=sinA+sinBsinA−sinB\frac{a+b}{a-b}=\frac{\sin A+\sin B}{\sin A-\sin B}a−ba+b=sinA−sinBsinA+sinB
A cubical box is kept on an inclined surface that makes an angle of 35° with the horizontal. Determine the force required to keep the box from sliding down if the weight of the box is 525 kg. (Assume there is no friction.)