# ENGG 202 Lecture Notes - Lecture 1: Hypotenuse, Quadratic Equation, Telephone Numbers In The United Kingdom

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Published on 26 Jan 2015

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ENGG 202 Assumed Knowledge - Solutions

Q1: For the right angled triangle shown, what is the length of side a?

Side c is 10 m and side b is 6 m.

Solution:

To determine the length of side a,

use Pythagorean’s Theorem (C2 = A2 + B2)

a

2 = 102 – 62

22

10 6 8am=−=

Q2: For the right angle triangle shown, what is angle A in degrees?

Side a is 8 m and side c is 10 m.

Solution:

For a right triangle, the ratio of the opposite side to the hypotenuse is the SIN of the angle.

8sin( )

10

8

arcsin 53.1

10

o

A

A

=

⎛⎞

==

⎜⎟

⎝⎠

Q3: For the non-right triangle shown, what is the length of side a?

Side b is 10 m and side c is 6 m. Angle A is 25 degrees.

Solution: Use the Cosine Law: c2 = a2 + b2 -2abCOS(C)

22

10 6 2(10)(6)cos25 5.22

o

am=+− =

Q4: For the non-right triangle shown, what is the angle C in

degrees? Side a is 5 m and side c is 8 m. Angle A is 30 degrees.

Solution: Use the Sine Law: sin sin sin

abc

A

BC

==

sin sin30

85

sin30

arcsin 8 53.1

5

o

oo

C

mm

Cm

=

⎛⎞

==

⎜⎟

⎝⎠

Q1,Q2

Q3,Q4

Q5: For the lever shown, and without calculating any angles:

a) Determine the lengths of arms BC and CD.

b) Find the coordinates of the midpoint of arm BC?

(assume C is 0,0)

c) If link AB is 2 in long, find the coordinates of

point A.

Solution:

a) either from Pythagorean’s rule or recognizing that both BC and CD are the hypotenuse of a 3-

4-5 triangle, the length BC is 5 in, and CD is 7.5 in (CD is a 3-4-5 triangle with multiples of

1.5 in).

b) The midpoint of BC is located halfway between B and C. since C is the 0,0 point and B is

located at (-4, 3) in, then the midpoint is located at (-2, 1.5) in.

c) Since BC is a 3-4-5 triangle with the 3 on the vertical and the 4 on the horizontal, the line

perpendicular to it (AB) is also a 3-4-5 with the 3 and 4 reversed (3 on the horizontal, 4 on the

vertical). In this case the hypotenuse has length 2 in and the ratios are: 2in/5 = x/3 = y/4

therefore the horizontal dimension of AB (x) is 1.2 in and the vertical dimension is 1.6 in.

The coordinates of point A are therefore (-4-1.2, 3-1.6) = (-5.2, 1.4) in.

If using the ratios is too confusing, then ensure you can solve it using the angles. Using the ratios

can just save you a bit of time if you know how to use them.

Q6: Determine the angle θ

You have to assume parallel lines or it is impossible to solve.

In all cases, the angle is 50o.

Q7: Determine the length of side AB if right angle ABC is

similar to right angle A'B'C'.

First determine the hypotenuse of A’B’C’: 22

15 36 39

=

+=

Using ratios: AB/13 = 15/39 AB = 5

AC/13 = 36/39 AC = 12