Question

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

10
10

0.07
0.07

1
1

0.7

Answer 1

Since θ and ϕ are acute angles of a right triangle, they are complementary, so sinθ = cosϕ. Thus

2x − 0.5 = x + 0.2
=> x = 0.7.

Answer: 0.7.