Question

In quadrant I, drawn a right triangle with one leg on the x-axis and its hypotenuse on the terminal side of drawn in standard position. If sin = 7/25, then what is the value of theta θ?

Right triangles and trigonometry
ANSWERED
asked 2020-11-07

In quadrant I, drawn a right triangle with one leg on the x-axis and its hypotenuse on the terminal side of drawn in standard position. If \(\sin = \frac{7}{25}\), then what is the value of \(\theta\)?

Answers (1)

2020-11-08

Since \(\sin \theta = \frac{opp}{hyp}\) then we let opp = 7 and hyp = 25.
We solve for adj (adjacent side) using Pythagorean Theorem:
\(opp^{2}+adj^{2}= hyp^{2}\)
\(7^{2}+adj=25^{2}\)
\(49+adj^{2}=625\)
\(adj^{2}=576\)
\(adj=24\)
Since  is in quadrant I, then tan theta is positive:
\(\tan \theta=\frac{opp}{adj}= \frac{7}{24}\)

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