The diagram shows a sketch of a survey done by a civil engineering student .find the value of x, giving your answer correct to 1 decimal place

You can do this by drawing one line through parallel to PQS to meet RQ at T

Now calculate length of RT:-

cos 70 = RT / 70 giving RT = 23.94m

sin 70 = ST/70 giving ST = 65.78 m

draw a line from S perpendicular to PQ to meet PQ at U.

PU = 110 - 65.78 = 44.22 m

tan 50 = SU / 44.22 giving SU = 52.70 m

TQ = SU = 52.70 m

So x = TQ + RT = 52.70 + 23.94 = 76.6 m to 1 dec place.

the sum of all the angles in a triangle are equal to 180

so you can add   the 3 given angles together to equal 180:

5y + 2y + 2y = 180

or since all three angles have the same letter, combine the 3 angles to equal 180:

9y = 180