basic_engineering_mathematics0

Geometry and triangles 141
Assignment 8
8. In Fig. A8.1, determine angles x, y and z (3)
This assignment covers the material contained in chapters
16 to 18. The marks for each question are shown
in brackets at the end of each question.
1. In the following equations, x and y are two related
variables and k and t are constants. For the stated equations
to be verified it is necessary to plot graphs of
the variables in modified form. State for each (a) what
should be plotted on the horizontal axis, (b) what should
be plotted on the vertical axis, (c) the gradient, and
(d) the vertical axis intercept.
Fig. A8.1
59° 37°
y
z
x
(i) y − k x = t (ii) y k = xt (8)
2. The following experimental values of x and y are
believed to be related by the law y = ax 2 + b, where
a and b are constants. By plotting a suitable graph
verify this law and find the approximate values of
a and b.
x 2.5 4.2 6.0 8.4 9.8 11.4
y 15.4 32.5 60.2 111.8 150.1 200.9
(8)
3. State the minimum number of cycles on logarithmic
graph paper needed to plot a set of values ranging from
0.065 to 480. (2)
9. In Fig. A8.2, determine angles a to e (5)
c e
a b
d 125°
60°
Fig. A8.2
10. In Fig. A8.3, determine the length of AC (4)
B
4. Determine the law of the form y = ae kx which relates
the following values:
y 0.0306 0.285 0.841 5.21 173.2 1181
x −4.0 5.3 9.8 17.4 32.0 40.0
(8)
D
3 m
A
10 m
C
5. Evaluate: 29 ◦ 17 ′ + 75 ◦ 51 ′ − 47 ◦ 49 ′ (3)
8 m
6. Convert 47.319 ◦ to degrees, minutes and seconds
(2)
7. State the angle (a) supplementary to 49 ◦
(b) complementary to 49 ◦ (2)
Fig. A8.3
11. Construct a triangle PQR given PQ = 5 cm,
∠QPR = 120 ◦ and ∠PRQ = 35 ◦ (5)