Question

tema: razones trigonométricas

1. halla o menciona el lado que se indica. utiliza las razones trigonométricas

1.)
35 m.
2.)
9.48 pulg.
3.)
59.12 cm.

Explanation:

Step1: Recall cosine formula for right - triangle

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. For the first triangle with $\theta = 52.8^{\circ}$ and adjacent side $a = 35$m, we want to find the hypotenuse $h$. So, $\cos(52.8^{\circ})=\frac{35}{h}$, then $h=\frac{35}{\cos(52.8^{\circ})}$.
$h=\frac{35}{\cos(52.8^{\circ})}\approx\frac{35}{0.604}\approx57.95$m.

Step2: Recall sine formula for right - triangle

In the second triangle with $\theta = 62^{\circ}$ and hypotenuse $h = 9.48$ inches, and we want to find the side opposite to the angle $\theta$. Using $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, so the opposite side $o=h\sin\theta$. Then $o = 9.48\times\sin(62^{\circ})$.
$o=9.48\times\sin(62^{\circ})\approx9.48\times0.883\approx8.37$ inches.

Step3: Recall tangent formula for right - triangle

In the third triangle with $\theta = 35.9^{\circ}$ and adjacent side $a = 59.12$cm, and we want to find the side opposite to the angle $\theta$. Using $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$, so the opposite side $o=a\tan\theta$. Then $o = 59.12\times\tan(35.9^{\circ})$.
$o=59.12\times\tan(35.9^{\circ})\approx59.12\times0.729\approx43.10$cm.

Answer:

1. Hypotenuse of first triangle is approximately $57.95$m.
2. Opposite side of second triangle is approximately $8.37$ inches.
3. Opposite side of third triangle is approximately $43.10$cm.