Question

A right triangle has two acute angles, θ
and ϕ
, so that sinθ=0.3x+0.2
and cosϕ=0.4x+0.4
. Use this information to find the value of x.(1 point)
Responses

0.2
0.2

−2

negative 2

2
2

6
6

Answer 1

Use sin θ = cos φ (the acute angles are complementary). So

0.3x + 0.2 = 0.4x + 0.4
=> 0.2 − 0.4 = 0.4x − 0.3x
=> −0.2 = 0.1x
=> x = −2.

(So x = −2.)