# Rectangular trapezoid

In a rectangular trapezoid ABCD with right angles at vertices A and D with sides a = 12cm, b = 13cm, c = 7cm. Find the angles beta and gamma and height v.

Result

v =  12 cm
B =  67.38 °
C =  112.62 °

#### Solution:

$a=12 \ \text{cm} \ \\ b=13 \ \text{cm} \ \\ c=7 \ \text{cm} \ \\ \ \\ x=a-c=12-7=5 \ \text{cm} \ \\ \ \\ v=\sqrt{ b^2 - x^2 }=\sqrt{ 13^2 - 5^2 }=12 \ \text{cm}=12 \ \text{cm}$
$B=\dfrac{ 180^\circ }{ \pi } \cdot \arcsin(v/b)=\dfrac{ 180^\circ }{ \pi } \cdot \arcsin(12/13) \doteq 67.3801 \doteq 67.38 ^\circ \doteq 67^\circ 22'49"$
$C=180-B=180-67.3801=\dfrac{ 5631 }{ 50 }=112.62=112.62 ^\circ =112^\circ 37'12"$

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
Pythagorean theorem is the base for the right triangle calculator.

## Next similar math problems:

1. RT - inscribed circle
In a rectangular triangle has sides lengths> a = 30cm, b = 12.5cm. The right angle is at the vertex C. Calculate the radius of the inscribed circle.
2. Sum of squares
The sum of squares above the sides of the rectangular triangle is 900 cm2. Calculate content of square over the triangle's hypotenuse.
3. Median in right triangle
In the rectangular triangle ABC has known the length of the legs a = 15cm and b = 36cm. Calculate the length of the median to side c (to hypotenuse).
4. A kite
ABCD is a kite. Angle OBC = 20° and angle OCD = 35°. O is the intersection of diagonals. Find angle ABC, angle ADC and angle BAD.
5. Isosceles trapezium
Calculate the area of an isosceles trapezium ABCD if a = 10cm, b = 5cm, c = 4cm.
6. Ditch
Ditch profile is an isosceles trapezoid with bases of length 80m and 60m. The slope of the side wall of the ditch is 80°. Calculate the ditch depth.
7. The ditch
Ditch with cross section of an isosceles trapezoid with bases 2m 6m are deep 1.5m. How long is the slope of the ditch?
8. Isosceles trapezoid
What is the height of an isosceles trapezoid, the base of which has a length of 11 cm and 8 cm and whose legs measure 2.5 cm?
9. Isosceles trapezoid
Calculate the area of an isosceles trapezoid whose bases are in the ratio of 4:3; leg b = 13 cm and height = 12 cm.
10. Right angle
If a, b and c are two sides of a triangle ABC, a right angle in A, find the value on each missing side. If b=10, c=6
11. Median
In triangle ABC is given side a=10 cm and median ta= 13 cm and angle gamma 90°. Calculate length of the median tb.