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

0.7
0.7

0.07
0.07

1
1

10

Answer 1

Since θ and ϕ are complementary (θ + ϕ = 90°), cosϕ = sinθ. So
x + 0.2 = 2x − 0.5
Solve: 0.7 = x.
Thus x = 0.7.