Year 10 5.3: the sine rule for angles (1 Viewer)

jane1820 · Oct 5, 2024

i dont get why the answer for 5.a. says that theta can be either 75 degrees or 117 degrees when the question specified that the angle is acute? i understand the ASTC rule which is: since sine is positive it can either be A (the angle itself) or S 180 - the angle
but i dont understand how the S is applicable here since the question said that theta is actue
is this a typo?

Study to success · Oct 5, 2024

Maybe it's because they want you to give the obtuse solution as well because sine can be obtuse when it is positive and can also be acute

nonya2000 · Oct 5, 2024

jane1820 said:
i dont get why the answer for 5.a. says that theta can be either 75 degrees or 117 degrees when the question specified that the angle is acute? i understand the ASTC rule which is: since sine is positive it can either be A (the angle itself) or S 180 - the angle
but i dont understand how the S is applicable here since the question said that theta is actue
is this a typo?
View attachment 44443 View attachment 44444

I know this textbook, it's New Century 10A

WeiWeiMan · Oct 5, 2024

jane1820 said:
i dont get why the answer for 5.a. says that theta can be either 75 degrees or 117 degrees when the question specified that the angle is acute? i understand the ASTC rule which is: since sine is positive it can either be A (the angle itself) or S 180 - the angle
but i dont understand how the S is applicable here since the question said that theta is actue
is this a typo?
View attachment 44443 View attachment 44444

cuz textbook solutions can be wrong

Luukas.2 · Oct 8, 2024

There are two answers to 5(a), but the second one is not 117^o, it is 21^o.

If the third angle is x (say) then:

$\frac{\sin{x}}{8}=\frac{\sin{42^\circ}}{6} \qquad \implies \qquad \sin{x} = \frac{4}{3} \times \sin{42^\circ} \approx 0.892174 ...$

There are two possible solutions:

$\text{Answer 1: } x = \sin^{-1}{0.892174...} \approx 63^\circ \qquad \implies \qquad \theta = 180^\circ\ -\ (63 + 42)^\circ = 75^\circ$

$\text{Answer 2: } x = 180^\circ\ -\ \sin^{-1}{0.892174...} \approx 117^\circ \qquad \implies \qquad \theta = 180^\circ\ -\ (117 + 42)^\circ = 21^\circ$

The answers have given the wrong angle for the second solution.

isho-3 · Oct 8, 2024

jane1820 said:
i dont get why the answer for 5.a. says that theta can be either 75 degrees or 117 degrees when the question specified that the angle is acute? i understand the ASTC rule which is: since sine is positive it can either be A (the angle itself) or S 180 - the angle
but i dont understand how the S is applicable here since the question said that theta is actue
is this a typo?
View attachment 44443 View attachment 44444

then the second answer is just wrong ig, somebody probably fucked up when editing and overlooked that

jane1820 · Oct 8, 2024

Luukas.2 said:
There are two answers to 5(a), but the second one is not 117^o, it is 21^o.

If the third angle is x (say) then:

$\frac{\sin{x}}{8}=\frac{\sin{42^\circ}}{6} \qquad \implies \qquad \sin{x} = \frac{4}{3} \times \sin{42^\circ} \approx 0.892174 ...$

There are two possible solutions:

$\text{Answer 1: } x = \sin^{-1}{0.892174...} \approx 63^\circ \qquad \implies \qquad \theta = 180^\circ\ -\ (63 + 42)^\circ = 75^\circ$

$\text{Answer 2: } x = 180^\circ\ -\ \sin^{-1}{0.892174...} \approx 117^\circ \qquad \implies \qquad \theta = 180^\circ\ -\ (117 + 42)^\circ = 21^\circ$

The answers have given the wrong angle for the second solution.

Yh me n my classmates were talking abt that
I ended up writing 75 degrees only

jane1820 · Oct 8, 2024

isho-3 said:
then the second answer is just wrong ig, somebody probably fucked up when editing and overlooked that

Fr fr like dont u literally get payed to write and edit textbooks? At least do ur job right (its not the first time)

Year 10 5.3: the sine rule for angles (1 Viewer)

jane1820

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