Gamma angle

Find the magnitude of the gamma angle in triangle ABC if: α = 38° 56 ’and β = 47° 54’.

Correct answer:

C =  93.1667 °

Step-by-step explanation:

$$\begin{gathered} A=38{\displaystyle \frac{56}{60}}=38+{\displaystyle \frac{56}{60}}={\displaystyle \frac{38\cdot 60+56}{60}}={\displaystyle \frac{2336}{60}}={\displaystyle \frac{584}{15}}\doteq 38.9333\text{ ° } \\ B=47{\displaystyle \frac{54}{60}}=47+{\displaystyle \frac{54}{60}}={\displaystyle \frac{47\cdot 60+54}{60}}={\displaystyle \frac{2874}{60}}={\displaystyle \frac{479}{10}}=47.9\text{ ° } \\ A+B+C=180\mathrm{°} \\ C=180-A-B=180-38.9333-47.9={\displaystyle \frac{559}{6}}\text{°}=93\frac{1}{6}\text{°}=93.1667\text{°}=93\mathrm{°}10^{\mathrm{\prime }} \end{gathered}$$

Try another example

Related math problems and questions:

• Triangles
  Find out whether given sizes of the angles can be interior angles of a triangle: a) 23°10',84°30',72°20' b) 90°,41°33',48°37' c) 14°51',90°,75°49' d) 58°58',59°59',60°3'
• Angles
  The triangle is one outer angle 158°54' and one internal angle 148°. Calculate the other internal angles of a triangle.
• Find the
  Find the third interior angle of the triangle ABC where: α = 48°, γ = 65°.
• Outer angles
  The outer angle of the triangle ABC at the A vertex is 71°40 ' outer angle at the vertex B is 136°50'. What size has the inner triangle angle at the vertex C?
• MO Z7–I–6 2021
  In the triangle ABC, point D lies on the AC side and point E on the BC side. The sizes of the angles ABD, BAE, CAE and CBD are 30°, 60°, 20° and 30°, respectively. Find the size of the AED angle.
• The triangles
  The triangles ABC and A'B'C 'are similar with a similarity coefficient of 2. The angles of the triangle ABC are alpha = 35°, beta = 48°. Determine the magnitudes of all angles of triangle A'B'C '.
• The two
  The two angles of a triangle are 78° and 82°. So what is the measure of the remaining third angle?
• Quotient
  Find quotient before the bracket - the largest divisor 51 a + 34 b + 68 121y-99z-33
• Main/central vertex
  ABC is an isosceles triangle with base BC and main vertex A. The angle at vertex A is 18°. What will be the size of the angle at vertex B?
• Rhombus angles
  If one angle in the rhombus is 159°, what is its neighboring angle in rhombus?
• Four multiples
  Four multiples of 6 he writes the following 12  24  56  72, which is correct?
• Box and whisker plot
  Construct a box and whisker plot for the given data. 56, 32, 54, 32, 23, 67, 23, 45, 12, 32, 34, 24, 36, 47, 19, 43
• Minute-hand
  How long distance will travel a large (minute) hand on the clock for 48 minutes, if its length is 56 cm?
• Angles
  In the triangle ABC, the ratio of angles is: a:b = 4: 5. The angle c is 36°. How big are the angles a, b?
• Speed of Slovakian trains
  Rudolf decided to take the train from the station 'Ostratice' to 'Horné Ozorovce'. In the train timetables found train Os 5409 : km 0 Chynorany 15:17 5 Ostratice 15:23 15:23 8 Rybany 15:27 15:27 10 Dolné Naštice 15:31 15:31 14 Bánovce nad Bebravou 15:35 1
• 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.
• Central angle
  What is the length of the arc of a circle with a diameter of 46 cm, which belongs to a central angle of 30°?