Question

solve for the missing sides of a right triangle with angle 24° and hypotenuse 13 inches. round your answers to the nearest hundredth. adjacent side: inches opposite side: inches question 2 1 pts solve for the missing angles in a right triangle with legs 13 and 25. round your answers to the nearest tenth of a degree. smaller angle: degrees larger angle: degrees

Explanation:

Step1: Find the adjacent side

Use the cosine function: $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$.
Given $\theta = 24^{\circ}$ and hypotenuse $c = 13$.
So, adjacent side $a=c\cos\theta=13\cos(24^{\circ})$.
Using a calculator, $\cos(24^{\circ})\approx0.9135$, then $a = 13\times0.9135=11.8755\approx11.88$.

Step2: Find the opposite side

Use the sine function: $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.
Opposite side $b=c\sin\theta=13\sin(24^{\circ})$.
Using a calculator, $\sin(24^{\circ})\approx0.4067$, then $b = 13\times0.4067 = 5.2871\approx5.29$.

Step1: Find the smaller angle

Let the legs be $a = 13$ and $b=25$. The smaller angle $\alpha$ is opposite the shorter leg.
Use the tangent function: $\tan\alpha=\frac{\text{opposite}}{\text{adjacent}}=\frac{13}{25}$.
$\alpha=\arctan(\frac{13}{25})$.
Using a calculator, $\alpha\approx27.5^{\circ}$.

Step2: Find the larger angle

The larger angle $\beta = 90^{\circ}-\alpha$.
$\beta=90 - 27.5=62.5^{\circ}$

Answer:

Adjacent Side: $11.88$ inches
Opposite Side: $5.29$ inches

---