Length + angle - math problems

Number of problems found: 186

Right angle
In a right triangle ABC with a right angle at the apex C, we know the side length AB = 24 cm and the angle at the vertex B = 71°. Calculate the length of the legs of the triangle.
Length of the arc
What is the length of the arc of a circle k (S, r=68mm), which belongs to a central angle of 78°?
ABCD
AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD
Circle and angle
What is the length of the arc of a circle with radius r = 207 mm with cental angle 5.33 rad?
Arc
Circle arc corresponding to angle is 32° is 28 dm long. What is the length of the entire circle?
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 depth angle 30° 30 '. Calculate the length of the bridge.
Side c
In △ABC a=2, b=4 and ∠C=100°. Calculate length of the side c.
Arc
The length of the circle is 41 amd arc length of the circle 9. What is the magnitude of the angle of this arc?
Similarity
Are two right triangles similar to each other if the first one has an acute angle 70°, and the second one has an acute angle 20°?
Clouds
Approximately at what height is the cloud we see under an angle of 26°10' and see the Sun at an angle of 29°15' and the shade of the cloud is 92 meters away from us?
30-60-90
The longer leg of a 30°-60°-90° triangle measures 5. What is the length of the shorter leg?
The mast
The top of the pole we see at an angle of 45°. If we approach the pole by 10 m, we see the top of the pole at an angle of 60°. What is the height of the pole?
The length
The length of the circle is 24 cm. What is the length of the circular arc of the corresponding angle 30°?
Central angle
What is the length of the arc of a circle with a diameter of 46 cm, which belongs to a central angle of 30°?
Mast
Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 13.3°. Determine the height of the mast, if the sun above the horizon is at angle 45°12'.
Aircraft
The plane flies at altitude 6500 m. At the time of first measurement was to see the elevation angle of 21° and second measurement of the elevation angle of 46°. Calculate the distance the plane flew between the two measurements.
Cuboid
Determine the dimensions of cuboid a, b, c; if diagonal d=9 dm has angle with edge a α=55° and has angle with edge b β=58°
Mast shadow
Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°. Use the law of sines.
Meridian
What is the distance (length) the Earth's meridian 23° when the radius of the Earth is 6370 km?
Depth angle
From a cliff of 150 meters high, we can see the ship at a depth angle of 9° at sea. How far is the ship from the cliff?