In ΔABC, leg AB has a measure of x, and leg BC has a measure of 14. Angle BCA has a measure of 32º. Find x.
What is 8.7?
100
A spectator looks up at an angle of 25º to the top of a building 500 feet away. How tall is the building?
What is 233 feet?
100
Given that xº is the measure of an acute angle, which of the following is equal to sin(xº)?
A. cos(xº)
B. cos(90-x)º
C. sin(90-x)º
D. tan(xº)
What is cos(90-x)º [B]?
200
In a right triangle, the ratio of the length of the leg opposite angle A to the length of the hypotenuse
What is sine?
200
The geometric mean of 4 and 12.25
What is 7?
200
In ΔABC, hypotenuse AC measures 28. Leg BC measures x. Angle BAC measures 61º. Find x.
What is 24.5?
200
A worker looks down from the top of a bridge 240 feet above a river at a barge. The angle of depression is 60º. How far is the barge from the base of the bridge?
What is 139 feet?
200
Mayuko is sitting 30 feet high in a football stadium. The angle of depression to the center of the field is 14º. What is the horizontal distance between Mayuko and the center of the field? Round to the nearest foot.
What is 120 feet?
300
The angle formed by a horizontal line and a line of sight to a point above
What is an angle of elevation?
300
If a right triangle has legs length a and b and a hypotenuse of length c, then a^2+b^2=c^2
What is the Pythagorean theorem?
300
In ΔLMK, hypotenuse KM measures 4.2 cm. Angle KML measures 18º. Find the perimeter of ΔLMK.
What is 9.5 cm?
300
The string of a flying kite is 360 feet long and makes a 40º angle with the ground. Find the altitude of the kite.
What is 231 feet?
300
You paddle a kayak due north at the rate of 2.5 mi/h. The river has a 2 mi/h current that flows due east. You want to find the kayak's direction.
What is 39º east of due north?
400
A ratio of two sides of a right triangle
What is a trigonometric ratio?
400
For ΔABC with side lengths a,b, and c, a/sin A = b/sin B = c/sin C
What is the law of sines?
400
A hiker whose eyes are 5.5 feet above the ground stands 25 feet from the base of a redwood tree. She looks up at an angle of 71º to see the top of the tree. To the nearest tenth of a foot, what is the height of the tree?
What is 78.1 feet?
400
The string of a flying kite is 360 feet long and makes a 40º angle with the ground. Find the horizontal distance between the kite flyer and the point on the ground directly below the kite.
What is 276 feet?
400
A sailboat sets out from shore, sailing due north at 10 mi/h. There is a crosswind blowing 5 mi/h in the direction 45º east of north. What is the speed of the sailboat?
What is 7 mi/h?
500
The endpoint of a vector
What is the terminal point of a vector?
500
For ΔABC with side lengths a, b, and c: a^2=b^2+c^2-(2bc∙cosA)
What is the law of cosines?
500
The hypotenuse of a right triangle measures 9 inches, and one of the acute angles measures 36º. What is the area of the triangle? Round to the nearest square inch.
What is 19 inches^2?
500
A helicopter pilot hovers 500 feet above a straight and flat road. The pilot looks down at two cars using 24º and 28º as angles of depression. How far apart are the cars? Explain your work.
What is 183 feet?
500
A plane is flying at a rate of 550 mi/h in the direction 40º east of north. There is a 30 mi/h crosswind blowing due south. What is the speed of the plane?