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Area of Non-Right Angled Triangles 2Area of Non-Right Angled Triangles 2
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Question 1 of 4
1. Question
Find the area of the non-right angled triangle below.
Round your answer to one decimal place- (11.25) `m^2`
Hint
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Incorrect
Area of a Non-Right Angled Triangle
`A_triangle=1/2``b``c``sin``A`where:
`a` is the side opposite angle `A``b` is the side opposite angle `B`
`c` is the side opposite angle `C`First, label the triangle.
Next, rewrite the Area formula based on the given values of the triangle.The formula needs two sides and one angle in between them (included angle).
`A_triangle=1/2``b``c``sin``A`Finally, substitute the values to the revised formula and solve for the area.`b=4.2`m`c=7.1`m`A=131°``A` `=` `1/2``b``c``sin``A` `=` `1/2(``4.2``)(``7.1``)sin``131°` Substitute the values `=` `1/2(29.82)sin131°` Evaluate `sin` `131` on your calculator `=` `14.91times0.7547096` `=` `11.2527` `=` `11.25 m^2` Rounded off to two decimal places `11.25 m^2` -
Question 2 of 4
2. Question
Find the area of the non-right angled triangle below.
Round your answer to two decimal places- (472.61) `cm^2`
Hint
Help VideoCorrect
Correct!
Incorrect
Area of a Non-Right Angled Triangle
`A_triangle=1/2``b``c``sin``A`where:
`a` is the side opposite angle `A``b` is the side opposite angle `B`
`c` is the side opposite angle `C`First, label the triangle.
Next, rewrite the Area formula based on the given values of the triangle.The formula needs two sides and one angle in between them (included angle).
`A_triangle=1/2``b``c``sin``A`Finally, substitute the values to the revised formula and solve for the area.`b=33`cm`c=29`cm`A=99°``A_triangle` `=` `1/2``b``c``sin``A` `=` `1/2(``33``)(``29``)sin``99°` Substitute the values `=` `1/2(957)sin99°` Evaluate `sin` `99` on your calculator `=` `478.5times0.98769` `=` `472.6088` `=` `472.61 cm^2` Rounded off to two decimal places `472.61 cm^2` -
Question 3 of 4
3. Question
Find the area of the non-right angled triangle below.
Round your answer to `2` decimal places- (305.06) `cm^2`
Hint
Help VideoCorrect
Great Work!
Incorrect
Area of a Non-Right Angled Triangle
`A_triangle=1/2``r``q``sin``P`where:
`r` is the side opposite angle `R`
`q` is the side opposite angle `Q`
`p` is the side opposite angle `P`First, label the triangle.
Next, rewrite the Area formula based on the given values of the triangle.The formula needs two sides and one angle in between them (included angle).
The included angle, `P`, is missing, but we can find it knowing that the sum of all interior angles in a triangle is `180°`. Subtract the other `2` known angles from `180°`.`180-(65+42)=180-107=``73°`
`A_triangle=1/2``r``q``sin``P`Finally, substitute the values to the revised formula and solve for the area.`r=22`cm`q=29`cm`P=73°``A_triangle` `=` `1/2``r``q``sin``P` `=` `1/2(``22``)(``29``)sin``73°` Substitute the values `=` `1/2(638)sin73°` Evaluate `sin` `73` on your calculator `=` `319times0.9563` `=` `305.06 cm^2` Rounded off to `2` decimal places `305.06 cm^2` -
Question 4 of 4
4. Question
Find the area of the non-right angled triangle below.
Round your answer to `2` decimal places- (92.66) `cm^2`
Hint
Help VideoCorrect
Excellent!
Incorrect
Area of a Non-Right Angled Triangle
`A_triangle=1/2``k``l``sin``J`where:
`j` is the side opposite angle `J``k` is the side opposite angle `K`
`l` is the side opposite angle `L`First, label the triangle.
Next, rewrite the Area formula based on the given values of the triangle.The formula needs two sides and one angle in between them (included angle).
The included angle, `J`, is missing, but we can find it knowing that the sum of all interior angles in a triangle is `180°`. Subtract the other `2` known angles from `180°`.`180-(38+79)=180-117=``63°`
`A_triangle=1/2``k``l``sin``J`Finally, substitute the values to the revised formula and solve for the area.`k=16`cm`l=13`cm`J=63°``A_triangle` `=` `1/2``k``l``sin``J` `=` `1/2(``16``)(``13``)sin``63°` Substitute the values `=` `1/2(208)sin63°` Evaluate `sin` `63` on your calculator `=` `104times0.891007` `=` `92.66 cm^2` Rounded off to `2` decimal places `92.66 cm^2`
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