Cosine + The Law of Cosines - practice problems - page 2 of 3
Number of problems found: 60
- Sides ratio and angles
In triangle ABC, you know the ratio of side lengths a:b:c=3:4:6. Calculate the angle sizes of triangle ABC. - Observer 64354
At what angle of view does an object 70 m long appear to the observer, 50 m away from one end, and 80 m from the other end? - A triangle 7
A triangle lot has the dimensions a=15m, b=10m, and c=20m. What is the measure of the angle between the sides of b and c? - SAS calculation
Given the triangle ABC, if side b is 31 ft., side c is 22 ft., and angle A is 47°, find side a. Please round to one decimal. - The pond
We can see the pond at an angle of 65°37'. Its endpoints are 155 m and 177 m away from the observer. What is the width of the pond? - Three 235
Three houses form a triangular shape. House A is 50 feet from house C and house B is 60 feet from house C. The measure is angle ABC is 80 degrees. Draw a picture and find the distance between A and B. - Children playground
The playground has a trapezoid shape, and the parallel sides have a length of 36 m and 21 m. The remaining two sides are 14 m long and 16 m long. Find the size of the inner trapezoid angles. - Two chords
From the point on the circle with a diameter of 8 cm, two identical chords are led, which form an angle of 60°. Calculate the length of these chords. - Viewing angle
The observer sees a straight fence 60 m long at a viewing angle of 30°. It is 102 m away from one end of the enclosure. How far is the observer from the other end of the enclosure? - Calculate 82578
The vertices of triangle ABC are: A[1, 2, -3], B[0, 1, 2], C[2, 1, 1]. Calculate the lengths of sides AB, AC and the angle at vertex A. - Three vectors
The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point to balance. Determine the angles of each two forces. - Calculate triangle
In the triangle, ABC, calculate the sizes of all heights, angles, perimeters, and area if given a=40cm, b=57cm, and c=59cm. - Space vectors 3D
The vectors u = (1; 3; -4), v = (0; 1; 1) are given. Find the size of these vectors, calculate the angle of the vectors, and the distance between the vectors. - Measurements of a triangle
Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary. A = 50°, b = 30 ft, c = 14 ft - Piece of a wire
A piece of wire is bent into the shape of a triangle. Two sides have lengths of 24 inches and 21 inches. The angle between these two sides is 55°. What is the length of the third side to the nearest hundredth of an inch? A: The length of the third side is - Triangle's centroid
In the triangle ABC the given lengths of its medians tc = 9, ta = 6. Let T be the intersection of the medians (triangle's centroid), and the point S is the center of the side BC. The magnitude of the CTS angle is 60°. Calculate the length of the BC side t - Parallelogram 65334
In a parallelogram, the sum of the lengths of the sides a+b = 234. The angle subtended by the sides a and b is 60°. The diagonal size against the given angle of 60° is u=162. Calculate the sides of the parallelogram, its perimeter, and its area. - Circumscribed 81759
In triangle ABC, we know a = 4 cm, b = 6 cm, γ = 60°. Calculate the area and radius of the inscribed and circumscribed circle. - Parallelogram
The sides of the parallelogram are 8 cm and 6 cm long, and the diagonals' angle is 60°. What is its area? - Inner angles
The inner angles of the triangle are 30°, 45°, and 105° and its longest side is 10 cm. Calculate the shortest side length, and write the result in cm up to two decimal places.
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