Planimetrics - math word problems - page 171 of 184
Number of problems found: 3667
- What is 19
What is the length of the hypotenuse c of a right triangle ABC if the angle α at vertex A is 30° and the hypotenuse a = 3cm?
- 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?
- Angles by cosine law
Calculate the size of the angles of the triangle ABC if it is given by: a = 3 cm; b = 5 cm; c = 7 cm (use the sine and cosine theorem).
- ISO trapezium
Calculate the area of an isosceles trapezoid with base 95 long, leg 27 long, and with the angle between the base and leg 70 degrees.
- EQL triangle
Calculate the inradius and circumradius of an equilateral triangle with side a=77 cm.
- Angles
Find the interior angles of a rhombus with area 72 cm² and perimeter 48 cm.
- Heron backlaw
Calculate the unknown side in a triangle with sides 39 and 38 and area 438.6.
- Triangle from median
Calculate the perimeter, area, and magnitudes of the triangle ABC's remaining angles: a = 8.4; β = 105° 35 '; and median ta = 12.5.
- Described 7872
In the KLM isosceles triangle, the KL base is 24 cm long, and the arm measures 15 cm. What is the radius of the circle described by this triangle?
- N-gon II
What is the side length of the regular 9-gon circumscribed circle of radius 13 cm?
- Construction 55311
Construct a KLM triangle where side k is 6.7 cm, the line to the k side is 4.1 cm, and the LKM angle is 63 degrees. Write the construction procedure.
- Construct 13581
The vertices of the triangle ABC lie on the circle k. The circle k is divided into three parts in a ratio of 1:2:3. Construct this triangle.
- Intersection of the altitudes
In the acute triangle KLM, the angle KLM is 68°. Point V is the intersection of the altitudes, and P is the foot of the altitude on the side LM. The angle P V M axis is parallel to the side KM. Compare the sizes of angles MKL and LMK.
- Hypotenuse 84015
In a right triangle ABC, the hypotenuse c = 8 cm and the side b = 4 cm. What is the size of angle α?
- Isosceles 4741
The arm is five times longer than its base in an isosceles triangle. Calculate its interior angles.
- Segments on the hypotenuse
A right triangle ABC has a hypotenuse of c=26cm. How many segments does the height vc=12 cm cut out on the hypotenuse c? What are the lengths of the sides a and b? What are the angles at the vertices A and B?
- Balloon and bridge
From the balloon, which is 92 m above the bridge, one end of the bridge is seen at a depth angle of 37° and the second end at a depth angle of 30° 30 '. Calculate the length of the bridge.
- 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.
- 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?
- The cable car
The cable car is 2610 m long and rises at an angle of 35°. Calculate the height difference between the lower and upper station of the cable car.
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