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

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 $$\theta$$?

2020-11-08

Since $$\sin \theta = \frac{opp}{hyp}$$ then we let opp = 7 and hyp = 25.
$$opp^{2}+adj^{2}= hyp^{2}$$
$$7^{2}+adj=25^{2}$$
$$49+adj^{2}=625$$
$$adj^{2}=576$$
$$adj=24$$
$$\tan \theta=\frac{opp}{adj}= \frac{7}{24}$$