Pythagorean theorem + analytic geometry - practice problems
Number of problems found: 101
- Trigonometric fx
When an acute angle φ is in the standard position, its terminal side passes through point P (1,3). Find trigonometric functions of angle θ : sin φ, cos φ, tan φ, cotan φ. - Find all 2
Find all the complex solutions (write the answer in the form x+iy) of the system. {|z-12|/|z-8i|=5/3 ; |z-4|=|z-8| - Triangle 82
Triangle PQR has vertices located at (2, 2), (5, -4), and (-4, -1). What type of triangle is triangle PQR? - The coordinates 3
The coordinates of two vertices of an equilateral triangle are (1,1) and (5,1). What are the coordinates of the third vertex?
- Line segment
Find the length of the line joining points A(-4,8) and B(-1,4). - Add vector
Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ. - A Cartesian framework
1. In a Cartesian framework, the functions f and g we know that: The function (f) is defined by f (x) = 2x², the function (g) is defined by g (x) = x + 3, the point (O) is the origin of the reference, and point (C) is the point of intersection of the grap - Two people
Two straight lines cross at right angles. Two people start simultaneously at the point of intersection. John walks at the rate of 4 kph on one road, and Jenelyn walks at the rate of 8 kph on the other road. How long will it take for them to be 20√5 km apa - Triangle
Plane coordinates of vertices: K[19, -4] L[9, 13] M[-20, 8] give Triangle KLM. Calculate its area and its interior angles.
- The fence
I'm building a cloth (board) fence. The boards are rounded in a semicircle at the top. The tops of the boards between the columns should copy an imaginary circle. The tip of the first and last board forms the chord of a circle whose radius is unknown. The - Suppose
Suppose you know that the length of a line segment is 15, x2=6, y2=14, and x1= -3. Find the possible value of y1. Is there more than one possible answer? Why or why not? - Two forces
The two forces, F1 = 580N and F2 = 630N have an angle of 59 degrees. Calculate their resultant force, F. - Crosswind
A plane is traveling 45 degrees N of E at 320 km/h when it comes across a current from S of E at 115 degrees of 20 km/h. What are the airplane's new course and speed? - Equation of the circle
Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3], and C[9, 4].
- Points on circle
The Cartesian coordinate system with the origin O is a sketched circle k /center O; radius r=2 cm/. Write all the points that lie on a circle k and whose coordinates are integers. Write all the points on the circle I with center O and radius r=5 cm, whose - Northeasterly 9681
A military unit marches in a northerly direction from point A to point B, 15 km away. From place B, it goes 12 km in a northeasterly direction to place C. Determine the direct distance of cities A and C and certainly the deviation -alpha- by which the uni - A man 7
A man wandering in the desert walks 3.8 miles in the direction of S 44° W. He then turns and walks 2.2 miles in the direction of N 55° W. At that time, how far is he from his starting point? (Round your answer to two decimal places.) - X-coordinate 81737
In triangle ABC, determine the coordinates of point B if you know that points A and B lie on the line 3x-y-5=0, points A and C lie on line 2x+3y+4=0, point C lies on the x-coordinate axis, and the angle at vertex C is right. - Construct 8
Construct an analytical geometry problem where it is asked to find the vertices of a triangle ABC: The vertices of this triangle are points A (1,7), B (-5,1) C (5, -11). The said problem should be used the concepts of distance from a point to a line, rati
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The Pythagorean theorem is the base for the right triangle calculator. Pythagorean theorem - practice problems. Analytic geometry - practice problems.