Children playground

The playground has the shape of a trapezoid, the parallel sides have a length of 36 m and 21 m, the remaining two sides are 14 m long and 16 m long. Determine the size of the inner trapezoid angles.

Result

A =  53.576 °
B =  66.868 °
C =  113.132 °
D =  126.424 °

Solution:

$a=36 \ \text{m} \ \\ c=21 \ \text{m} \ \\ b=14 \ \text{m} \ \\ d=16 \ \text{m} \ \\ \ \\ x=a-c=36-21=15 \ \text{m} \ \\ \Delta x,b,d \ \\ \ \\ b^2=x^2+d^2 - 2xd \cos A \ \\ \ \\ A=\dfrac{ 180^\circ }{ \pi } \cdot \arccos( \dfrac{ x^2+d^2-b^2 }{ 2 \cdot \ x \cdot \ d } )=\dfrac{ 180^\circ }{ \pi } \cdot \arccos( \dfrac{ 15^2+16^2-14^2 }{ 2 \cdot \ 15 \cdot \ 16 } ) \doteq 53.5764 \doteq 53.576 ^\circ \doteq 53^\circ 34'35"$

$B=\dfrac{ 180^\circ }{ \pi } \cdot \arccos( \dfrac{ x^2+b^2-d^2 }{ 2 \cdot \ x \cdot \ b } )=\dfrac{ 180^\circ }{ \pi } \cdot \arccos( \dfrac{ 15^2+14^2-16^2 }{ 2 \cdot \ 15 \cdot \ 14 } ) \doteq 66.8676 \doteq 66.868 ^\circ \doteq 66^\circ 52'3"$

$C=180 - B=180 - 66.8676=113.132=113.132 ^\circ =113^\circ 7'55"$

$D=180 - A=180 - 53.5764=126.424=126.424 ^\circ =126^\circ 25'26"$

Try calculation via our triangle calculator.

Try another example

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

Showing 0 comments:

Be the first to comment!

Next similar math problems:

1. Trapezoid - RR
   Find the area of the right angled trapezoid ABCD with the right angle at the A vertex; a = 3 dm b = 5 dm c = 6 dm d = 4 dm
2. 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.
3. Largest angle of the triangle
   Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a
4. Isosceles triangle 10
   In an isosceles triangle, the equal sides are 2/3 of the length of the base. Determine the measure of the base angles.
5. Triangle and its heights
   Calculate the length of the sides of the triangle ABC, if v_a=5 cm, v_b=7 cm and side b is 5 cm shorter than side a.
6. Greatest angle
   Calculate the greatest triangle angle with sides 197, 208, 299.
7. ABCD
   AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD
8. Side c
   In △ABC a=2, b=4 and ∠C=100°. Calculate length of the side c.
9. Scalene triangle
   Solve the triangle: A = 50°, b = 13, c = 6
10. Theorem prove
    We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
11. The pond
    We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond?
12. 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).
13. Bisectors
    As shown, in △ ABC, ∠C = 90°, AD bisects ∠BAC, DE⊥AB to E, BE = 2, BC = 6. Find the perimeter of triangle △ BDE.
14. Laws
    From which law follows directly the validity of Pythagoras' theorem in the right triangle? ?
15. The spacecraft
    The spacecraft spotted a radar device at altitude angle alpha = 34 degrees 37 minutes and had a distance of u = 615km from Earth's observation point. Calculate the distance d of the spacecraft from Earth at the moment of observation. Earth is considered
16. 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?
17. Height 2
    Calculate the height of the equilateral triangle with side 38.