Answer:
- See a hypothetical example and complete explantion below.
Explanation:
Hello! As a friend of mine says: remember to ask complete and clear questions to obtain good and precise answers to exactly what you want to know.
Since the use of trigonometric ratios to find the lentgth of a side of a triangle is a common exmple in mathematics, and an important skill to develop to do many calculations, I can help you with my own example.
The tangent ratio is defined for a right triangle as:
[tex]tangent(\alpha )=\dfrac{\text{length of the opposite leg to the angle}}{\text{length of the adjacent leg to the angle}}[/tex]
Then, you need the angle and the length of one of the legs to find the length of the other leg.
Assuming a hypothetical triangle PQR with these features:
- m ∠ P = 30º
- m ∠ Q = 90º (the right angle)
- m ∠ R = 60º (from 180º - 90º - 30º = 60º)
- Length of leg PQ = 10 inches
You can find the length of side QR in this way:
[tex]tangent(30\º)=\dfrac{\text{length of QR}}{\text{length of PQ}}\\ \\ \\ \text{length of QR}=}{\text{length of PQ}}\times tant(30\º)[/tex]
[tex]\text{length of QR}=10inches\times \sqrt{3}/3\approx 5.8inches[/tex] ← answer
The result is rounded to the nearest tenth.
