# Goniomentry and trigonometry - math word problems

1. Angle of deviation
The surface of the rotating cone is 30 cm2 (with circle base), its surface area is 20 cm2. Calculate the deviation of the side of this cone from the plane of the base.
2. Baker
The baker makes from 10 kg of flour 12 kg dough. How much flour he need to make a 100 kg dough?
3. Study
For 7 hours study, she scored a 75 so if she made 93 how many hours would she need to study?
4. Angles by cosine law
Calculate the size of the angles of the triangle ABC, if it is given by: a = 3 cm; b = 5 cm; c = 7 cm (use the sine and cosine theorem).
5. Four sides of trapezoid
In the trapezoid ABCD is |AB| = 73.6 mm; |BC| = 57 mm; |CD| = 60 mm; |AD| = 58.6 mm. Calculate the size of its interior angles.
6. Driver
The driver of the supply car reckoned that at the average speed of 72 km/h arrives to the warehouse for 1 1/4 hours. After 30 km however unintentionally drove to the gas station and have ten minutes delay. At what average speed would have to go the rest
7. Tree
Between points A and B is 50m. From A we see a tree at an angle 18°. From point B we see the tree in three times bigger angle. How tall is a tree?
8. Right triangle trigonometrics
Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent)
9. 30-gon
At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area.
10. V-belt
Calculate a length of the V-belt when the diameter of the pulleys is: D1 = 600 mm D2 = 120 mm d = 480 mm
11. Sun rays
If the sun's rays are at an angle 60° then famous Great Pyramid of Egypt (which is now high 137.3 meters) has 79.3 m long shadow. Calculate current height of neighboring chefren pyramid whose shadow is measured at the same time 78.8 m and the current he
12. Candies
There are red, blue and green candies in bad. Red to green is in 6:11 ratio and blue to red in a 7: 5 ratio. In what proportion are blue to green candies?
13. How far
From the top of a lighthouse 145 ft above sea level, the angle of depression of a boat 29°. How far is the boat from the lighthouse?
14. Rhombus
One angle of a rhombus is 136° and the shorter diagonal is 8 cm long. Find the length of the longer diagonal and the side of the rhombus.
15. 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 figure.
16. Triangle ABC v2
Area of the triangle is 12 cm square. Angle ACB = 30º , AC = (x + 2) cm, BC = x cm. Calculate the value of x.
17. Four sided prism
Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50 degree angle with the base plane.
18. Pentagon
Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 cm.
19. Regular n-gon
Which regular polygon have a radius of circumscribed circle r = 10 cm and the radius of inscribed circle p = 9.962 cm?
20. Cuboids
Two separate cuboids with different orientation in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62955056, 0.094432584, 0.77119944) u2=(0.14484653, 0.9208101, 0.36211633)

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Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.