Question

Can someone please help me find the value of p and q?

Answer 1

`q=31.7\\p=28.4`

Doing all calculations with 3 significant figures.

Explanation:

First, we'll obtain the value of 'q', this by realizing how the two angles together form a right triangle with inner angles of 30, 60, 90.

Furthermore, the opposite side of the angle of 30 is 'q' and its adjacent is given as 55. Hence, we can solve for 'q' using tangent as follows:

`tan(30)=(q)/(55) =.577`

We solve for 'q':

`q=.577*55=31.7`

Now to solve for 'p', we first will calculate what '55-p' is equal to.

First, we realize '55-p' corresponds to the adjacent side to the angle of 50 inside the small right triangle (the one with inner angles of 50, 40, 90) and q (which we now know is 31.7) correspond to the opposite side. Hence, we again use tangent as follows:

`tan(50)=(q)/(55-p) =(31.7)/(55-p) =1.19`

We solve for 'p':

`1.19(55-p)=31.7\\65.5-1.19p=31.7\\1.19p=33.8\\p=(33.8)/(1.19)=28.4`