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. 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.
4. Greatest angle
   Calculate the greatest triangle angle with sides 197, 208, 299.
5. ABCD
   AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD
6. Two groves
   Two groves A, B are separated by a forest, both are visible from the hunting grove C, which is connected to both by direct roads. What will be the length of the projected road from A to B, if AC = 5004 m, BC = 2600 m and angle ABC = 53° 45 ’?
7. Scalene triangle
   Solve the triangle: A = 50°, b = 13, c = 6
8. Side c
   In △ABC a=2, b=4 and ∠C=100°. Calculate length of the side c.
9. Inner angles
   The inner angles of the triangle are 30°, 45° and 105° and its longest side is 10 cm. Calculate the length of the shortest side, write the result in cm up to two decimal places.
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. Viewing angle
    The observer sees a straight fence 60 m long at a viewing angle of 30°. It is 102 m away from one end of the enclosure. How far is the observer from the other end of the enclosure?
12. 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?
13. The angle of view
    Determine the angle of view at which the observer sees a rod 16 m long when it is 18 m from one end and 27 m from the other.
14. Triangle from median
    Calculate the perimeter, content, and magnitudes of the remaining angles of triangle ABC, given: a = 8.4; β = 105° 35 '; and median ta = 12.5.
15. 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).
16. Laws
    From which law follows directly the validity of Pythagoras' theorem in the right triangle? ?
17. Bisectors
    As shown, in △ ABC, ∠C = 90°, AD bisects ∠BAC, DE⊥AB to E, BE = 2, BC = 6. Find the perimeter of triangle △ BDE.