Question

Please EXPLAIN how to get this answer so I can do it with other problems. A straight answer would be great, but I have to do about 30 more problems like these, so I'd like to know how to do it with an explanation! It doesn't have to be long, just so I can understand it. (This is for geometry by the way)

Answer 1

Answer:

PQ = 3.58, and RQ = 10.4

Step-by-step explanation:

We are given the hypotenuse of the triangle, and an angle. Use sin and cos to solve.  

Hypotenuse = 11,

Opposite side is PQ

Adjacent side is RQ

x = 19

Sin x  = (opposite side)/(hypotenuse)

Cos x = (adjacent side)/(hypotenuse)

For PQ, this is the side opposite to the angle, so use sin,

Sin 19 = x/11

   11(Sin 19) = x

        3.58 = x        (rounded to the nearest hundredth)            

For RQ, this is the side adjacent to the angle, so use cos,

Cos 19 = x/11

   11(Cos 19) = x

        10.4 = x        (rounded to the nearest hundredth)