Arcsine - practice problems

The arcsine is the inverse of the trigonometric sine function. The argument of the function is a number (ratio of the length of the opposite side to the hypotenuse), and the output is the angle in radians.

Task: Work through each problem with care and demonstrate your solution process for each one.

Number of problems found: 62

Angle of inclination
Find the angle of inclination of a ramp that rises 80 cm over a horizontal length of 200 cm.
Triangle 90
A triangle has sides of 6 cm, 4.5 cm, and 7.5 cm. What are the sizes of its angles?
Parallelogram 44
Parallelogram ABCD has an area of 32 cm², |AB| = 8 cm, |BC| = 5 cm. Calculate the sizes of its interior angles.
In a regular 5
In a regular triangular prism ABCV, the angle between the lateral face and the base plane is α = 45°. Determine the angle between the lateral edge and the base plane.
Graduation of the track
The gradient of the track is 9 per mille, and the distance along the slope [AC] is 560 m. Determine angle alpha and the distance [AB], which is the height between A and B. A / | B/____________C
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?
Chord 24
A chord of length t = r√2 divides a circle with radius r into two circular segments. What is the ratio of the areas of these two segments?
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.
Central angle
A circle k with a center at point S and a radius of 6 cm is given. Calculate the size of the central angle subtended by a chord 10 cm long.
Kite deltoid angles
A paper kite is shaped like a deltoid ABCD, with two shorter sides 30 cm long, two longer sides 51 cm long, and a shorter diagonal 48 cm long. Determine the sizes of the internal angles of the given deltoid.
In plane 2
Triangle ABC lies in the plane with a right angle at vertex C, where A(1, 2), B(5, 2), C(x, x+1), and x > −1. a) Determine the value of x. b) Determine the coordinates of point M, the midpoint of segment AB. c) Prove that vectors AB and CM are perpendi
Archaeologists
Archaeologists need to find out the size of the vessel if the sherd found was in the shape of a circular section with a length of 12 cm and a height of 3 cm. What is the area of this section?
Quadrilateral triangle segment
The quadrilateral ABCD is symmetrical about the diagonal AC. The length of AC is 12 cm, the length of BC is 6 cm, and the interior angle at vertex B is right. points E and F are given on the sides AB, and AD so that the triangle ECF is equilateral. Determ
Felix
Calculate how much land Felix Baumgartner saw after jumping from 36 km above the ground. The radius of the Earth is R = 6378 km.
Acceleration - down a slope
A skier goes down a slope 66 m long in a uniformly accelerated motion in 10 seconds. With what acceleration was it moving, and what is the slope of the slope?
The cosine law
Solve the unknown dimensions for the following triangle: Triangle ABC: Angle A=43 degrees, b=7.0 cm, c=6.0 cm Question 1. Angle B with units written as degrees Question 2. Angle C with units written as degrees Question 3. a, rounded to the nearest tenth o
A rhombus 4
A rhombus has a side length of 10 cm. Find the angles at each vertex of the rhombus if the shorter diagonal measures 7 cm. Give your answers to the nearest degree and provide clear geometric reasoning at each step.
Colored area
How large is the area colored brown inside a square of side 6 cm if each of the four brown circular segments is from a circle with a radius of the length of the square's side? The length of the circular segments is equal to the length of the side of the s
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 =? °
Rectangle ABCD
The rectangle ABCD is given whose | AB | = 5 cm, | AC | = 8 cm, ∢ | CAB | = 30°. How long is the other side, and what is its area?

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