# Rectangle

Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees.

Result

|GN| =  13.29 cm
|QN| =  28.31 cm

#### Solution:

$\alpha = 28^\circ \ \\ a = |HN| = 25 \ cm \ \\ \tan \alpha = \dfrac{ b }{ a } \ \\ \ \\ b = |GN| = a \tan \alpha = 13.29 \ \text { cm }$
$\cos \alpha = \dfrac{ a }{ u } \ \\ u= |QN| = \dfrac{ a }{ \cos \alpha } = 28.31 \ \text { cm }$

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

#### Following knowledge from mathematics are needed to solve this word math problem:

Pythagorean theorem is the base for the right triangle calculator. See also our trigonometric triangle calculator.

## Next similar math problems:

1. IS triangle
Calculate interior angles of the isosceles triangle with base 38 cm and legs 26 cm long.
Between cities A and B is route 13 km long of stúpanie average 7‰. Calculate the height difference of cities A and B.
3. Trapezoid MO
The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
4. Right triangle
Calculate the missing side b and interior angles, perimeter and area of ​​a right triangle if a=10 cm and hypotenuse c = 16 cm.
5. Regular 5-gon
Calculate area of the regular pentagon with side 7 cm.
6. Church tower
Archdeacon church in Usti nad Labem has diverted tower by 186 cm. The tower is 65 m high. Calculate the angle by which the tower is tilted. Result write in degree's minutes.
7. Angle between lines
Calculate the angle between these two lines: ? ?
8. Mast
Mast has 17 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 9.3°. Determine the height of the mast, if the sun above the horizon is at angle 44°30'.
9. Q-Exam
If tg α = 0.9, Calculating sin α, cos α, cotg α .
10. 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.
11. Steeple
Steeple seen from the road at an angle of 75°. When we zoom out to 25 meters, it is seen at an angle of 20°. What is high?
12. Two forces
Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.
13. Trigonometric functions
In right triangle is: ? Determine the value of s and c: ? ?
14. Right
Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?
15. Height difference
What height difference overcome if we pass road 1 km long with a pitch21 per mille?