Right Triangles & Trigonometry: Finding Sides and Angles

Question:

In triangle PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.

Answer:

Based on the given triangle, Sin P = 1/5, Cos P = (2/5)√(150), and tan P = (√(6))/12.

Let's start by drawing a diagram of triangle PQR. Q is the right angle, so label it as such. If PQ = 5 cm and PR + QR = 25 cm, we can find the values of sin P, cos P, and tan P by utilizing the Pythagorean theorem.

First, we need to find the length of QR using the Pythagorean theorem: PR² = PQ² + QR². By substituting the known values, we can calculate QR = √(PR² - 25) = √(600).

Next, we can determine the values of sin P, cos P, and tan P using the formulas. After finding PR = 25, we simplify the expressions to sin P = 1/5, cos P = (2/5)√(150), and tan P = (√(6))/12.

Understanding trigonometry and right triangles can help solve various real-world problems and phenomena. By mastering these concepts, you can navigate complex situations with ease.