Arcsine - practice problems - page 3 of 4

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

Number of problems found: 62

Ladder slope
What is the slope of a ladder 6.2 m long and 5.12 m in height?
Isosceles triangle
An isosceles triangle with base c and arms a is given by: a = 50.3 cm c = 48.2 cm Determine the interior angles and heights of the base c.
V-belt
Calculate the length of the V-belt when the diameter of the pulleys is: D1 = 600 mm D2 = 120 mm d = 480 mm (distance between pulley axes)
Ratio iso triangle
The ratio of the sides of an isosceles triangle is 7:6:7. Find the base angle to the nearest answer correct to 3 significant figures.
Angle in RT
Determine the size of the smallest internal angle of a right triangle whose sides are consecutive terms of an arithmetic progression.
Cablecar
Funicular on Petrin (Prague) was 408 meters long and overcame the difference of 106 meters in altitude. Calculate the angle of the climb.
Medians of isosceles triangle
The isosceles triangle has a base ABC |AB| = 16 cm and a 10 cm long arm. What is the length of the medians?
Church tower
Archdeacon church in Usti nad Labem has diverted the tower by 186 cm. The tower is 65 m high. Calculate the angle by which the tower is tilted. Results are written in degree minutes.
Circular pool
The pool's base is a circle with a radius r = 10 m, excluding a circular segment that determines the chord length of 10 meters. The pool depth is h = 2 m. How many hectoliters of water can fit into the pool?
Isosceles triangle
What are the angles of an isosceles triangle ABC if its base is long a=7 m and has an arm b=9 m?
Climb
The road sign that informs the climb is 10.3%—the car drives 10 km along this road. What is the height difference that the car went?
Sine
In the triangle Δ ABC, if sin α =0.6 and sin β =0.7 Calculate sin γ.
Observer
The observer sees a straight fence 100 m long in 30° view angle. From one end of the fence is 119 m. How far is it from the other end of the fence?
IS triangle
Calculate the interior angles of the isosceles triangle with base 12 cm and legs 19 cm long.
Angles
Find the interior angles of a rhombus with area 72 cm² and perimeter 48 cm.
Trapezoid MO
Right-angled trapezoid ABCD has a right angle at vertex B. Given that |AC| = 12, |CD| = 8, and the diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid.
Forces
At point G, three mutually perpendicular forces act: F₁ = 16 N, F₂ = 7 N, and F₃ = 6 N. Determine the resultant force F and the angles between F and each of F₁, F₂, and F₃.
Right
Determine the angles of a right triangle with hypotenuse c and legs a and b, if: 2a +5b = 5.283c
Heron backlaw
Calculate the length of the unknown side of a triangle with sides 39 and 38 and area 438.6.
Black building
Jozef built a building with a rectangular footprint of 3.9 m × 6.7 m. Calculate by what percentage the building exceeds the legal limit of 25 m² for a small building. A building constructed without planning permission is called an illegal building. Also c

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