Everything Maths Grade 10

K 8 G

84 ◦

H

10

9

L

J

5

Calculate the length ofJK.

25.The figure below shows triangleGHKwith the smaller triangleJKLsitting inside of it. Furthermore,
the following lengths and angles are given:GH= 12;LJ= 7;HJ= 8;LG= 11;K^= 33◦. The figure
is drawn to scale.

K

33 ◦

11 G

H

8

12

L

J

7

Find the length ofKL.

26.In the diagram below,Pis the mid-point ofN QandRis the mid-point ofM Q. One side of the triangle

has a given length of

z

2

2.

Q M

N

z

2 ^2

R

P

a)Determine the value ofP Rin terms ofz.

b)You are now told thatP Rhas a length of 2. What is the value ofz?

27.The figure below shows△M N Qcrossed byRP. PointsPandRbisect their respective sides of the

triangle.

N Q

M

8 b

P

R

119 ◦

a)With the two angles given,M^= 8band\N P R= 119◦, determine the value ofQ^in terms ofb.

b)You are now told thatM^has a measure of 76 ◦. Determine for the value ofb. Give your answer as

an exact fractional value.

Chapter 7. Euclidean geometry 279