Question

In triangle PUG with right angle at U, sin P = cos ___

Answer 1

In a right triangle with a right angle at U, the sine of angle P is equal to the cosine of angle G.

Step-by-step explanation:

In the right triangle PUG, with a right angle at U, the sine of angle P is equal to the cosine of angle G. This is because in a right triangle, the sine of one angle is equal to the cosine of the other acute angle.

Since angle U is the right angle, angles P and G are complementary, meaning they add up to 90 degrees. Therefore, the sine of angle P is equal to the cosine of the complementary angle G. In mathematical terms, this is an application of the trigonometric identity sin(90° - θ) = cos(θ).

So, the complete statement is sin P = cos G, with angle G being the complement of angle P in triangle PUG.