Question

In ΔPQR, sin R = align="absmiddle" class="latex-formula">. What is cos P?
(a) $\frac{5}{3}$

(b) $\frac{3}{4}$

(c) $\frac{4}{3}$

(d) $\frac{3}{5}$


(image attached below)

Answer 1

Answer:

Since we know that ΔPQR is a right triangle, we can also asume that:

sin R = cos P = 3/5

So the answer is (d).

* This formular can also be applied to other right triangles.

In a right triangle, sine of one acute angle will always be equal to cosine of the other acute angle.

And we can check this by actually finding cos P using the lengths of the sides, by calculating PR first:

PR = √(PQ² + RQ²) = √(12² + 16²) = 20

=> cos P = PQ/PR = 12/20 = 3/5