Planimetrics - math word problems - page 176 of 183
Number of problems found: 3656
- Tangent of an angle
Suppose the tangent of an angle of a right-angled triangle is 0.8. Then its longest side is: - Goniometric form
Determine the goniometric form of a complex number z = √ 110 +4 i. - Isosceles 7661
The area of the isosceles triangle is 8 cm2, and its arm's length is 4 cm. Calculate the sizes of its interior angles. - Airplane navigation
An airplane leaves an airport and flies west 120 miles and then 150 miles in the direction S 32.12°W. How far is the plane from the airport (round to the nearest mile)? - Third roots
Determine the sum of the three complex third roots of the number 64 . - Triangle and its heights
Calculate the length of the sides of the triangle ABC if va=13 cm, vb=15 cm and side b are 5 cm shorter than side a. - Determine 3882
Determine the sum of the three square roots of 343.
- In plane 2
A triangle ABC is located in the plane with a right angle at vertex C, for which the following holds: A(1, 2), B(5, 2), C(x, x+1), where x > -1. a) determine the value of x b) determine the coordinates of point M, which is the midpoint of line segment - Mast shadow
The mast has a 13 m long shadow on a slope rising from the mast foot toward the shadow angle at an angle of 15°. Determine the height of the mast if the sun above the horizon is at an angle of 33°. Use the law of sines. - Ratio in trapezium
The ratio of the height v and the base a, c in the trapezoid ABCD is 1:6:3. Its area is 324 square cm, and the peak angle B is 35 degrees. Determine the perimeter of the trapezoid. - Circular railway
The railway connects points A, B, and C in a circular arc, whose distances are | AB | = 30 km, AC = 95 km, and BC | = 70 km. How long will the track be from A to C? - Coefficient 81704
In the equation of the line p: ax-2y+1=0, determine the coefficient a so that the line p: a) it formed an angle of 120° with the positive direction of the x-axis, b) passed through point A[3,-2], c) was parallel to the x-axis, d) had a direction of k = 4. - Parametrically 6400
Find the angle of the line, which is determined parametrically x = 5 + t y = 1 + 3t z = -2t t belongs to R and the plane, which is determined by the general equation 2x-y + 3z-4 = 0. - Modulus and argument
Find the mod z and argument z if z=i - Area 51
The area of the triangle is 54.39, alpha is 32 °, and gamma is 144 °.
- Perimeter - triangle
Construct triangle ABC when we know a + b + c (perimeter), height to side c, and angle gamma. - Equilateral 7962
After a long dinner, inside a lounge in the shape of a square ABCD, a drunken shopper E lies in such a way that the triangle DEC is equilateral. Spy F lies on the edge of BC, with |EB|=|EF|. What is the size of the angle CEF? - A drone
A flying drone aimed the area for an architect. He took off perpendicularly from point C to point D. He was 300 m above ABC's plane. The drone from point D pointed at a BDC angle of 43°. Calculate the distance between points C and B in meters. - Map - climb
On the map of the High Tatras, on a scale of 1:11000, are cable car stations in the Tatranska Lomnica and the Skalnate Pleso with a distance of 354.6 mm. The altitude of these stations is 949 m and 1760 m. What is the average angle of climb on this cable - Trapezoid MO
The rectangular trapezoid ABCD with the right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid.
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