Question

How to do Q1 a and b

(Please wait for me to attach the picture)

Answer 1

The figures are too small to see the given dimensions. Perhaps you can enlarge it and repost.

Answer 2

Find the unknown marked lengths and angles in the following figures

Answer 3

how many questions are you asking?

Answer 4

Part a.)

PR = 3 + 4 = 7
cos R = 7/12
R = arccos(7/12) approx = 54.3147°
180° in a triangle, so m<PQR approx = 35.6853
Save that for later.

Pythag thm:
7² + QP² = 12²
QP² = 144 - 49
QP approx = 9.7468

tan <PQS approx = 3/9.7468
Take arctan.
m<PQS approx = 17.1080


n = m<SQR - m<PQS = 35.6853 - 17.1080 = 18.5773
*note* all equals are approx here --^

n approx = 18.5773

Part b.)

Pythag thm -> QS = 10
Given RQ = QS so RQ = 10
RP = RQ + QP = 18, save for later

tan <QSP = 8/6
Take arctan of both sides.
m<QSP approx = 53.1301

tan <RSP = 18/6
Take arctan of both sides.
m<RSP approx = 71.5651

θ = m<RSP - m<QSP = 71.5651 - 53.1301 = 18.4350
*note* all equals are approx here --^

@Luis Rivera, if the 6-8-10 triangle were a 30-60-90, then it's sides would be in a ratio of 1:sqrt(3):2, which they are not.