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Word Problems
Solving for Sides
Solving for Angles
Solving Area
100
Point A is 100 ft on a horizontal line from point B. Point C, on a line with a 20 degree rise from the horizontal, is 80 ft. from point B. Find the distance from A to C.
177.299
100
A triangular walking course has 2 sides of 230 feet and 360 feet, and the angle between these sides measures 38º. Find the length of the third side of the course.
228.04 ft.
100
Solve for angle X given that x= 14, y= 20, and z= 12.
Angle X= 43.531°
100
In ABC, AB = 10, AC = 8, and measure of angle A = 45º. Find the area of ABC.
28.284
200
To approximate the length of a lake, a surveyor starts at one end of the lake and walks 245 yards. He then turns 110ºW and walks 270 yards until he arrives at the other end of the lake. Approximately how long is the lake?
296 yds.
200
In triangle DEF, side e = 8 cm, f = 10 cm, and the angle at D is 60°. Find side d.
9.165 cm
200
Solve for angle A given that a= 25, b= 32, and c= 37.
Angle A= 41.701°
200
In an isosceles , the two equal sides each measure 24 meters, and they include an angle of 30º. Find the area of the isosceles triangle.
144 m²
300
After the hurricane, the small tree in my neighbor’s yard was leaning. To keep it from falling, we nailed a 6-foot strap into the ground 4 feet from the base of the tree. We attached the strap to the tree 3½ feet above the ground. How far from vertical was the tree leaning?
16.1º past vertical (=106.1º)
300
In a rhombus whose side measures 22 m and the smaller angle is 55º, find the length of the larger diagonal
39.028 m
300
Three sides of a triangle measure 20m, 30m, and 40m. Find the largest angle of the triangle.
x= 104.478°
300
In a rhombus, each side is 15, and one angle is 130º. Find the area of the rhombus.
172.360
400
You are heading to Beech Mountain for a ski trip. Unfortunately, state road 105 in North Carolina is blocked off due to a chemical spill. You have to get to Tynecastle Highway which leads to the resort at which you are staying. NC-105 would get you to Tynecastle Hwy in 12.8 miles. The detour begins with a 18 veer off onto a road that runs through the local city. After 6 miles, there is another turn that leads to Tynecastle Hwy. Assuming that both roads on the detour are straight, how many extra miles are you traveling to reach your destination?
You travel 0.532 miles. In the original diagram, x = 7.33 miles
400
In the oblique triangle ABC, find side b if side a = 5 cm, c = square root of 2 cm, and they include and angle of 45°
4.123 cm
400
Find Angle C given a=9, b= 5, and c= 8.
Angle C= 62.182°
400
Find the area of triangle BRU if b= 12, r= 8, u= 16, and angle U= 48°
35.671
500
Two ships leave port at 4 p.m. One is headed at a bearing of N 38 E and is traveling at 11.5 miles per hour. The other is traveling 13 miles per hour at a bearing of S 47 E. How far apart are they when dinner is served at 6 p.m.?
36.2 mi.
500
In the oblique triangle PQR, find side r if side p = 5 in, q = 10 in, and they include and angle of 14°.
7.616 in.
500
Find Angle Q given p= 8.1 q= 6.3, and r= 9.6
Angle Q= 40.601°
500
Find the area if one side of a parallelogram is 8 in and the other side is 5 in with an angle of 110°.
18.794 in²