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]
[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]
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[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]
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[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]
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[tex]\bold{FINAL\:ANSWERS:}[/tex]
- angle G = 56 degrees
- side g = 20.73 units
- side f = 13.98 units
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[tex]\tiny\textsf{Note that the answers are rounded off to the nearest hundredths}[/tex]
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