Download Sketch a series of triangles and then work out the values of eight

Sketch a series of triangles and then work out
the values of eight unknown angles. Give each
final answer correct to the nearest angle but
keep ‘working’ values to full calculator accuracy.
When you have worked out the eight angles you
will be able to de-code this message:
83°, 30°, 20°, 36°, 20°, 56°, 83°, 39°, 30°, 30°,
20°, 61°, 20°, 19°.
Triangle STU has ST = 8cm.
Find the size of the angle at E in triangle DEF
Triangle ABC has BC = 11cm.
US = 12cm.
Find the size of the angle at I.
Triangle PQR has the angle at Q equal to 53°.
DF = 7cm.
AB = 5cm
Triangle DEF has the angle at D equal to 80°.
Find the size of the angle at G in triangle EFG
Triangle HIJ has HJ = 7cm.
Find the size of the angle at C.
AC = 14cm.
Find the size of the angle at R.
TU = 10cm.
Find the size of the angle at S.
EF = 11cm.
Find the size of the angle at T.
The angle at J is equal to 36°
PR = 8cm.
Find the size of the acute angle at F.
PQ = 5cm.
DF is extended to point G, so that FG = 8cm.
IH = 12cm
Trig Code
Team game involving Sine and Cosine Rules
12 cards to be divided between 3 or 4 pupils.
Each has to contribute to solution of the problem, which is on one of the cards.
Solution:
B
5cm
cos C = 112 + 142 - 52
2 x 11 x 14
11cm
C = 18.54………°
C = 19°
A
14cm
E
?
C
sin E = sin 80° x 7
11
?
11cm
80°
D
?
?
7cm
F
G
I
12cm
H
7cm
Q
5cm
p
?
36°
?
2
EG2 = 112 + 82 – 2 x 11 x 8 x cos (80 + 38.80….)
EG = 16.42……….. cm
sin G = sin 118.80… ° x 11
16.42….
G = 35 .93…….°
G = 36°
sin I = sin 36° x 7
12
I = 20.05…..°
I = 20°
sin R = sin 53° x 5
8
R = 29.94…..°
R = 30°
J
53°
8cm
E = 38.80…….°
E = 39°
F = (180 –( 80 + 38.80….))°
F = 61°
R
2
cos S = 12 + 8 - 10
2 x 8 x 12
T
S = 55.77……
S = 56°
sin T = sin 55.77….° x 12
10
83° 30° 20° 36° 20° 56°
T R I G
I S
?
8cm
?
T = 82.81….°
S
T = 83°
83° 39° 30° 30° 20° 61° 20° 19°
T E R R I F I C
10cm
12cm
U