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Given: FGH is a right triangle. H is the right angle. h = 25 units, F = 34 degrees.
Solve for: angle G, side gand side f
pls pls answer kailangan ko​

Given FGH Is A Right Triangle H Is The Right Angle H 25 Units F 34 DegreesSolve For Angle G Side Gand Side Fpls Pls Answer Kailangan Ko class=

Sagot :

SOLVING RIGHT TRIANGLE

☞ Solving a triangle means finding the measures of all its angles and sides.

[tex]\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}[/tex]

[tex]\bold{GIVEN:}[/tex]

  • FGH is a right triangle
  • H is the right angle
  • h = 25 units
  • F = 34 degrees

[tex]\bold{SOLVE\:FOR:}[/tex]

  • angle G
  • side g
  • side f

[tex]\bold{SOLUTION:}[/tex]

[tex]\textsf{Solving for angle G:}[/tex]

  • The sum of the interior angles of a triangle is 180°, thus,

[tex]\quad\qquad\tt m\angle F + m\angle G + m\angle H = 180° \\ \\ \quad\qquad\tt 34°+m\angle G+90°= 180 °\\ \\\quad \qquad\tt 124°+m\angle G=180° \\ \\\quad \qquad\tt m\angle G=180°-124° \\ \\ \quad \qquad \red{\boxed{ \tt m \angle G=56°}}[/tex]

[tex]\\[/tex]

[tex]\textsf{Solving for side g:}[/tex]

  • We will use the given measure of angle F and the ratio of cosine.

[tex] \qquad\tt cos\: F= \frac{adjacent}{hypotenuse} \\ \\ \qquad\tt cos \: 34= \frac{g}{25} \\ \\ \qquad\tt (25)(cos \: 34)=\bigg( \frac{g}{\cancel{25}} \bigg)(\cancel{25}) \\ \\ \qquad \tt g = (25)(cos \: 34) \\ \\ \qquad \red{ \boxed{ \tt g = 20.73\:units}}[/tex]

[tex]\\[/tex]

[tex]\textsf{Solving for side f:}[/tex]

  • We will still use the given measure of angle F but this time, we will use the ratio of sine.

[tex] \qquad\tt sin\: F= \frac{opposite}{hypotenuse} \\ \\ \qquad\tt sin \: 34= \frac{f}{25} \\ \\ \qquad\tt (25)(sin \: 34)=\bigg( \frac{f}{\cancel{25}} \bigg)(\cancel{25}) \\ \\ \qquad \tt f = (25)(sin\: 34) \\ \\ \qquad \red{ \boxed{ \tt f= 13.98\:units}}[/tex]

[tex]\\[/tex]

[tex]\bold{FINAL\:ANSWERS:}[/tex]

  • angle G = 56 degrees
  • side g = 20.73 units
  • side f = 13.98 units

[tex]\\[/tex]

[tex]\tiny\textsf{Note that the answers are rounded off to the nearest hundredths}[/tex]

[tex]\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}[/tex]

[tex]\\[/tex]

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