This document contains 10 math word problems involving geometry concepts like triangles, angles, distances, and areas. Problem 6 asks to calculate the angle formed by a point above a triangle and the area of the plane formed. Problem 7 asks about the angles and possible positions of tents set up in a triangle configuration. Problem 8 involves calculating angles, lengths, and surface areas of a glass pyramid block.

1. 268
BAB
9
CHAPTER
9
6. In the diagram on the right, PQR is an equilateral triangle with sides
of 6 cm and lies on a horizontal plane. Point T is 4 cm vertically
above the midpoint of PQ. Calculate PL5
(a) the angle formed by TR and triangle PQR,
(b) the area of plane TPR.
7. A group of girl scouts took part in a camping. They set up three
tents with the positions as shown in the diagram on the right.
The positions of the three tents formed a triangle ABC. PL5
(a) Calculate the obtuse angle ACB.
(b) Draw and label another triangle other than triangle ABC
which shows the possible position of tent C such that the
distance AB and AC and ∠ABC remain unchanged.
(c) Tent C has to be relocated to other position but the distance
between tent A and tent B and angle BAC formed between
the tents remain unchanged. Calculate the distance AC
such that only one triangle can be formed.
8. The diagram on the right shows a glass block in the shape of a
pyramid VABC. The base of the block is an isosceles triangle and
AB = AC = 5.2 cm. V is the vertex of the block such that
BV = CV = 3 cm. The angle between the inclined plane VBC and
the base ABC is 50°. Calculate PL5
(a) ∠BAC, given the base area is 8.69 cm2
,
(b) the length of AV, given the angle between the line AV and
the base is 25°,
(c) the surface area of VAB of the glass block.
9. Rashid drove a boat westwards. He noticed a lighthouse at a distance of 25 km away at the
bearing of 235°. PL5
(a) Sketch a diagram to illustrate the above situation.
(b) What is the distance travelled by the boat if its distance from the lighthouse is 16 km?
(c) Rashid continued to drive the boat until his distance from the lighthouse is 16 km again.
(i) Calculate the distance between the first position and the second position of the boat.
(ii) What is the bearing of the lighthouse from the boat when the boat is at the second
position?
10. The diagram on the right shows the positions of four petrol stations,
J, K, L and M in a district. Given the distance JK = 40 km,
KL = 80 km, LM = 65 km and ∠JKL = 44°. PL5
(a) Calculate
(i) the distance JL, (ii) ∠JML,
(iii) the area of KLM.
(b) Without doing calculations, determine the petrol
station which is the furthest from petrol station K.
Explain.
(c) If a car travels along the road KL, calculate the shortest distance of the car from petrol
station M.
T
Q
R
P
6 cm
6 cm
B
A C
7 m
8 m
50°
A
B
C
V
M
J
K
40 km
65 km
80 km L