A right triangle has two acute angles, $ heta$ and $\phi$, so that $\cos \phi = x + 0.2$ and $\sin heta = 2

Question

A right triangle has two acute angles, $	heta$ and $\phi$, so that $\cos \phi = x + 0.2$ and $\sin 	heta = 2x - 0.5$. What is the value of $x$?Answer Choices0.071010.7

GPT-5 mini · Answer

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

(Check: cos φ = 0.9 and sin θ = 0.9, both valid.)

A right triangle has two acute angles, $\theta$ and $\phi$, so that $\cos \phi = x + 0.2$ and $\sin \theta = 2x - 0.5$. What is the value of $x$?Answer Choices0.071010.7

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