Angle - math word problems - page 27 of 64

Number of problems found: 1279

Diamond cutoff angle
Find the cut-off angle for the diamond-air pair. n_d = 2.42 α_m =? The absolute refractive index of light for air n = 1
Semicircle
Calculate the length of a semicircle with a radius of 6 cm.
Pentadecagon
Calculate the area of a regular 15-side polygon inscribed in a circle with a radius r = 4. Express the result to two decimal places.
Dodecagon
Calculate the size of the smaller angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1 A2A3. .. A12. Express the result in degrees.
An observer
An observer standing west of the tower sees its top at an altitude angle of 45 degrees. After moving 50 meters to the south, he sees its top at an altitude angle of 30 degrees. How tall is the tower?
The tower
The observer sees the tower's base 96 meters high at a depth of 30 degrees and 10 minutes and the top of the tower at a depth of 20 degrees and 50 minutes. How high is the observer above the horizontal plane on which the tower stands?
Diamond area calculation
The ABCD diamond has a circumference of 72 cm. The longer diagonal of the animal with the line segment AB angle is 30 °. Calculate the area of the ABCD diamond.
Two chords
From the point on the circle with a diameter of 8 cm, two identical chords are led, which form an angle of 60°. Calculate the length of these chords.
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.
Triangle in a square
In a square ABCD with side a = 6 cm, point E is the center of side AB, and point F is the center of side BC. Calculate the size of all angles of the triangle DEF and the lengths of its sides.
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.
Triangle height construction
A. Construct ∆ABC such that c = 55 mm, α = 45 °, β = 60 °. B. Draw any acute triangle and construct its heights.
Traffic sign
There is a traffic sign for climbing on the road with an angle of 7%. Calculate at what angle the road rises (falls).
Fighter
A military fighter flies at an altitude of 10 km. The ground position was aimed at an altitude angle of 23° and 12 seconds later at an altitude angle of 27°. Calculate the speed of the fighter in km/h.
The right triangle
In the right triangle ABC with a right angle at C, we know the side lengths AC = 9 cm and BC = 7 cm. Calculate the length of the remaining side of the triangle and the size of all angles.
Isosceles triangle
Calculate the size of the interior angles and the length of the base of the isosceles triangle if the arm's length is 17 cm and the height of the base is 12 cm.
Hexagon area calculation
Calculate the area of a regular hexagon inscribed in a circle with a radius r = 7 cm.
TV tower
Calculate the height of the television tower if an observer standing 430 m from the base of the tower sees the peak at an altitude angle of 23°.
The ladder
The ladder touches a wall at the height of 7.5 m. The angle of the inclination of the ladder is 76°. How far is the lower end of the ladder from the wall?
Triangle angle
An isosceles triangle has the size of the angles at the base alpha = beta = 34 degrees 34 minutes. Calculate the magnitude of the angle at the remaining vertex of the triangle in degrees and minutes.

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