Pythagorean theorem + angle - practice problems - page 6 of 13
Number of problems found: 258
- Center of gravity
In the isosceles triangle ABC is the ratio of the lengths of AB and the height to AB 10:12. The arm has a length of 26 cm. If the center of gravity is T, find the area of the triangle ABT. - Pentagon
Calculate the length of a regular pentagon's side, circumference, and area, inscribed in a circle with a radius r = 6 cm. - Perpendicular 67174
Calculate the perpendicular s in the right triangle STU (the right angle at the vertex U), if the hypotenuse is long u = 93cm and the perpendicular t = 48 cm - Hexagon 8167
How many dm² of organic glass is needed to produce 50 washers in the shape of a regular hexagon? The side is 8 cm long.
- Diamond ABCD
In the diamond ABCD, the diagonal e = 24 cm, and the size of angle SAB is 28 degrees, where S is the intersection of the diagonals. Calculate the circumference of the diamond. - Diagonals of the rhombus
How long are the diagonals e, and f in the diamond if its side is 5 cm long and its area is 20 cm²? - Right triangle trigonometrics
Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60°, and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent) - 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 - Clock's 38311
How far apart are the tips of the clock's hands in 3 hours if the larger hand is 124 mm long and the smaller 75 mm?
- Embankment 7879
An embankment 7.5 m high should be built on the horizontal plane. The width of the upper surface of the embankment is 2.9 m, and the slope is 35 °. What will be the lower width of the embankment? - Acceleration 2
If a car traveling at a velocity of 80 m/s/south accelerated to a speed of 100 m/s east in 5 seconds, what is the car's acceleration? Using Pythagorean theorem - Track arc
Two straight tracks are at an angle 74°. They will join with a circular arc with a radius r=1127 m. How long will the arc be connecting these lines (L)? How far is the arc's center point from track crossings (x)? - 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. - Calculate 6219
Right triangle. Given: side b = 15.8 angle alpha = 15° 11`. Calculate the side a, c, beta angle, and area.
- Trapezoid RT
The plot has a shape of a rectangular trapezium ABCD, where ABIICD with a right angle at the vertex B. side AB has a length of 36 m. The lengths of the sides AB and BC are in the ratio 12:7. Lengths of the sides AB and CD are a ratio of 3:2. Calculate con - Determine 83083
A 6.5-meter-long ladder rests against a vertical wall. Its lower end rests on the ground 1.6 meters from the wall. Determine how high the top of the ladder reaches and at what angle it rests against the wall. - Loonie
Loonie has three wooden sticks measuring 17 inches, 21 inches, and 25 inches. He lays them down to form a triangle. Find the measure of the angle enclosed by 17 inches and 21 inches. (Express answers to the nearest hundredths) (using the law of cosines) - Cosine
Cosine and sine theorem: Calculate all missing values (sides and angles) of the triangle ABC. a = 20 cm; b = 15 cm; γ = 90°; c =? cm; α =? °; β =? ° - Five circles
On the line segment CD = 6 there are five circles with one radius at regular intervals. Find the lengths of the lines AD, AF, AG, BD, and CE.
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