Planimetry - math word problems - page 68 of 72
Number of problems found: 1438
- Tower's view
From the church tower's view at 65 m, the top of the house can be seen at a depth angle of alpha = 45° and its bottom at a depth angle of beta = 58°. Calculate the house's height and its distance from the church. - Segments on the hypotenuse
A right triangle ABC has a hypotenuse c = 26 cm. The altitude from C to the hypotenuse is h_c = 12 cm. What are the lengths of the two segments of the hypotenuse? What are the lengths of sides a and b? What are the angles at vertices A and B? - Perimeter of a circle segment
A circle with a diameter of 30 cm is cut by a chord t = 16 cm. Calculate the perimeter and area of the smaller segment. - Triangle tangent area
The tangent of the angle formed by the adjacent sides of the triangle ABC (side a=29 m, b = 40 m) equals 1.05. Calculate the area of that triangle. - Big tower
From a tower 15 meters high and 30 meters away from the river, the width of the river appeared at an angle of 15°. How wide is the river in this place? - Circumscribed decagon
In a regular decagon, the diameter of the circumscribed circle measures 10 cm. Determine the radius of the circle inscribed in this decagon. - Triangle area angle
The area of a right triangle ABC is 346 cm2, and the angle at vertex A is 64°. Calculate the lengths of the overhangs a and b. - Diamond height angle
What is the height of a diamond with a side 6 cm long if the angle formed by the sides is 78 degrees and 10 '? - View angle - river The 15 m high building is 30 m away from the river bank. The river's width can be seen from the roof of this building at an angle of 15°. How wide is the river?
- Diamond and angles
The interior angles of the rhombus are 60° and 120°. Its side is 5 cm long. Find the area of the rhombus. - Factory chimney
How tall is a factory chimney if its top is seen from a distance of 60 metres at an elevation angle of 60°? - Cis notation
Evaluate the multiplication of two complex numbers in cis notation: (6 cis 120°)(4 cis 30°) Write the result in cis and Re-Im notation. - Cosine
Cosine and sine theorem: Calculate all unknown values (sides and angles) of the triangle ABC. a = 20 cm; b = 15 cm; γ = 90°; c =? cm; α =? °; β =? ° - Calculate 5
Calculate the area and perimeter of a trapezoid with side a = 10, angle α = 40°, angle β = 50°, and side c = 3. - Apex of the Isosceles triangle
The angle at the apex of an isosceles triangle is 78°. The base is 28.5 cm long. What is the shoulder length? - View angle
We see the tree on the opposite bank of the river at an angle of 15° from a distance of 41 meter from the river bank. From the bank of the river, we can see at an angle of 31°. How tall is the tree? - Parallelogram - angle alfa
In the parallelogram ABCD the length of sides are AB = 8, BC = 5, BD = 7. Calculate the magnitude of the angle α = ∠DAB (in degrees). - Trapezoids
In the isosceles trapezoid ABCD we know: AB||CD, |CD| = c = 8 cm, height h = 7 cm, |∠CAB| = 35°. Find the area of the trapezoid. - Rectangle and squares
A 9 cm × 15 cm rectangle is divided into unit squares. How many paths are there from one rectangle vertex to the opposite vertex if one can only go to the right and up the sides of the squares? - The ladder
The ladder makes an angle of 2°30' with the wall and reaches a height of 2.3 m. How far is the ladder from the wall?
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