I Have Questions. You've Got The Answers. 5

If $A, B,$ and $C$ are the angles of a triangle such that

$5 \sin A + 12 \cos B = 5$

and

$12 \sin B + 5 \cos A = 2$

then the measure of angle $C$ is

$a. 150^\circ$

$b. 135^\circ$

$c. 45^\circ$

$d. 30^\circ$

#Geometry

Easy Math Editor

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Comments

No solution exists.

Hint: $(5\sin A + 12\cos B)^2 + (12\sin B + 5\cos A)^2 = 5^2 + 2^2$ .

Hint 2: Apply $\sin^2 x + \cos^2 x =1$ , $\sin(x + y) = \sin x \cos y + \cos x \sin y$ .

Hint 3: If $A,B,C$ are indeed the angles of a triangle, then what is the possible range of $\sin (A+B)$ ?

Hint 4: Show that $0 < \sin (A+B) \leq 1$ is not fulfilled.

Pi Han Goh - 3 years, 7 months ago

Thanks!

Benedict Dimacutac - 3 years, 7 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$