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

1
1

0.07
0.07

10
10

0.7

Answer 1

In a right triangle the acute angles are complementary, so sin θ = cos φ. Thus
2x − 0.5 = x + 0.2 → x = 0.7.

Answer: 0.7