Answer:
5. 24°
6. 30°
7. 49°
Step-by-step explanation:
5. You are given right triangle with known opposite leg and hypotenuse. By the sine definition,
[tex]\sin \theta=\dfrac{\text{opposite leg}}{\text{hypotenuse}}=\dfrac{11}{27}\\ \\\theta=\sin^{-1}\left(\dfrac{11}{27}\right)\approx 24^{\circ}[/tex]
6. You are given right triangle with known opposite leg and hypotenuse. By the sine definition,
[tex]\sin \theta=\dfrac{\text{opposite leg}}{\text{hypotenuse}}=\dfrac{12}{24}=\dfrac{1}{2}\\ \\\theta=\sin^{-1}\left(\dfrac{1}{2}\right)\approx 30^{\circ}[/tex]
7. You are given right triangle with known adjacent leg and hypotenuse. By the cosine definition,
[tex]\cos \theta=\dfrac{\text{adjacent leg}}{\text{hypotenuse}}=\dfrac{13}{20}\\ \\\theta=\cos^{-1}\left(\dfrac{13}{20}\right)\approx 49^{\circ}[/tex]
