Question

A right triangle has two acute angles, θ
and ϕ
, so that cosϕ=x+0.2
and sinθ=2x−0.5
. What is the value of x?(1 point)
Responses

0.07
0.07

0.7
0.7

10
10

1
1

Answer 1

In a right triangle the acute angles are complementary, so sinθ = cosφ. Thus
2x − 0.5 = x + 0.2 ⇒ x = 0.7.
(Check: cosφ = sinθ = 0.9, within [0,1].)