# Right triangle

Calculate the length of the remaining two sides and the angles in the rectangular triangle ABC if a = 10 cm, angle alpha = 18°40'.

Result

A =  18.667 °
B =  71.333 °
C =  90 °
a =  10 cm
b =  29.6 cm
c =  31.244 cm

#### Solution:

$A=18+40/60=\dfrac{ 56 }{ 3 } \doteq 18.6667 \doteq 18.667 ^\circ \doteq 18^\circ 40'$
$B=90-A=90-18.6667=71.333=71.333 ^\circ =71^\circ 19'59"$
$C=90=90 ^\circ$
$a=10 \ \text{cm}$
$\tan A=a/b \ \\ b=a/\tan( A ^\circ \rightarrow\ \text{rad} )=a/\tan( A ^\circ \cdot \ \dfrac{ \pi }{ 180 } \ )=10/\tan( 18.6666666667 ^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ )=29.59985=29.6 \ \text{cm}$
$c=\sqrt{ a^2+b^2 }=\sqrt{ 10^2+29.5999^2 } \doteq 31.2436 \doteq 31.244 \ \text{cm}$

Try calculation via our triangle calculator.

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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

Be the first to comment!

Tips to related online calculators

## Next similar math problems:

1. 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)
2. Right triangle
It is given a right triangle angle alpha of 90 degrees beta angle of 55 degrees c = 10 cm use Pythagorean theorem to calculate sides a and b
3. Triangle
Calculate the area of right triangle ΔABC, if one leg is long 14 and its opposite angle is 59°.
4. Height 2
Calculate the height of the equilateral triangle with side 38.
5. Steps
Find the height between the two floors if you know that the number of steps between the two floors is 18, the gradient is 30º and the length of the step is 28.6 cm. Report the result in centimeters to the nearest centimeter.
6. 30-60-90
The longer leg of a 30°-60°-90° triangle measures 5. What is the length of the shorter leg?
7. The cable car
The cable car has a length of 3,5 kilometers and an angle of climb of 30 degrees. What is the altitude difference between Upper and Lower Station?
8. Cable car
Cable car rises at an angle 45° and connects the upper and lower station with an altitude difference of 744 m. How long is "endless" tow rope?
The ladder has a length of 3 m and is leaning against the wall, and its inclination to the wall is 45°. How high does it reach?
10. Chord MN
Chord MN of circle has distance from the center circle S 120 cm. Angle MSN is 64°. Determine the radius of the circle.