Question

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)

A) 10°
B) 35°
C) 55°
D) 80°

Answer 1

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

Answer 2

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= (100)/(10)`

`x=10`°

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

the answer is
β=35°