Angle + ratio - practice problems
Number of problems found: 104
- The angles 4
The angles of a triangle are divided into the ratio 126: 213: 312. If the three angles sum to 180°, find the size of each of the three angles. - The number 10
The number of sides of two regular polygons differ by 1 the sum of the interior angles of the polygons is in the ratio of 3:2 calculate the number of sides of each polygon. - Minute angle
Find the size of the angle, which takes a minute hand for 20 minutes. - Gear wheels
Two gear wheels, which fit together, have the number of teeth z1=117 and z2=70. Calculate the speed of the first wheel if the second wheel rotates 582 revolutions per minute.
- Refractive index
The light passes through the interface between air and glass with a refractive index of 1.5. Find: (a) the angle of refraction if light strikes the interface from the air at an angle of 40°. (b) the angle of refraction when light hits the glass interface - Angles
In the triangle ABC, the ratio of angles is α:β = 4:5. The angle γ is 36°. How big are the angles α and β? - Powerplant chimney
From the building window at the height of 7.5 m, we can see the top of the factory chimney at an altitude angle of 76° 30 ′. We can see the chimney base from the same place at a depth angle of 5° 50 ′. How tall is the chimney? - 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 an angle 45°12'. - Calculate
Calculate the area of triangle ABC if given by alpha = 49°, beta = 31°, and the height on the c side is 9cm.
- Similarity
The area of the regular 10-gon is 563 cm². The area of similar 10-gon is 606 dm². What is the coefficient of similarity? - Right-angled 81150
In the right-angled triangle ABC (the right angle at vertex C), the angle ratio is α : β = 5 : 3. Calculate the sizes of these angles and convert them to degrees and minutes (e.g., 45°20') - (tangent) 21633
Based on the fact that you know the values of sin and cos of a given angle and you know that tan (tangent) is their ratio, determine d) tan 120 ° e) tan 330 ° - Observer
The observer sees a straight fence 100 m long in 30° view angle. From one end of the fence is 102 m. How far is it from another end of the fence? - Isosceles 71154
Calculate all interior angles in the isosceles triangle ABC if we know that BC is the base, and we also know: | ∢BAC | = α; | CABCA | = 4α
- Calculate 4422
Calculate the perimeter of the triangle ABC if a = 12 cm, the angle beta is 38 degrees, and the gamma is 92 degrees. - The angles ratio
The angles in the ABC triangle are in the ratio 1:2:3. Find the angles' sizes and determine what kind of a triangle it is. - Isosceles triangle 8
If the rate of the sides of an isosceles triangle is 7:6:7, find the base angle correct to the nearest degree. - Angles of the triangle
ABC is a triangle. The size of the angles alpha and beta are in a ratio of 4:7. The angle gamma is greater than the angle alpha by a quarter of a straight angle. Determine angles of the triangle ABC. - Angles ratio
In an ABC triangle, is true relationship c is less than b, and b is less than a. Internal angles of the triangle are in the ratio 5:4:9. The size of the internal angle beta is:
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