Krism
Answered

Angles ∝ and β are the two acute angles in a right triangle. Use the relationship between sine and cosine to find the value of β if β < ∝.


sin(7x - 15) = cos(3x + 5)

A10°
B35°
C55°
D80°

Verified Answer :

miner3mj

Ok so cos(x) = sin(90-x) so using that you can get sin(7x-15) = sin(90-(3x+5)) so 7x-15 = -3x+85. 10x = 100 and x = 10. Use that to find the 2 angles are 55 and 35

calculista

we know that
in a right triangle
(∝ + β)=90°-------> by complementary angles
so
sin ∝ = cos β
\(sin(7x - 15) = cos(3x + 5)\)
Let 
∝=7x-15
β=3x+5

therefore

\((7x-15)+(3x+5)=90 \\ 10x-10=90 \\ 10x=90+10 \\ x= \frac{100}{10}\)
\(x=10\)°

∝=7x-15-----------> ∝=\(7*10-15\)-------> ∝=55°
β=3x+5------------> β=\(3*10+5\)-------> β=35°

the answer is
 β=35°

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