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find side x, correct to two decimal places
x = 20.74
find side x, correct to two decimal places
x = 20.76
find side x, correct to one decimal place
x = 12.8
find side x, correct to one decimal place
x = 16.2
find side x, correct to one decimal place
x = 37.7
find side x, correct to one decimal place
x = 59.6
find the angle θ, correct to one decimal place:
sin θ = 0.4817
28.8°
find the angle θ, correct to one decimal place:
cos θ = 0.6275
51.1°
find the angle θ, correct to one decimal place:
tan θ = 0.8666
40.9°
find the anlge θ, correct to one decimal place:
cos θ = 0.9564
17.0°
find the unknown angle θ, correct to one decimal place
32.2°
find the unknown angle θ, correct to one decimal place
55.8°
find the unknown angle θ, correct to one decimal place
46.6°
find the unknown angle θ, correct to one decimal place
58.8°
find the unknown angle θ, correct to one decimal place
32.2°
find the missing angle θ, correct to one decimal place
41.2°
find the value of θ, correct to one decimal place
36.9°
how?
h=5, o=3
sinθ= o÷h
= 0.6000
θ=sin(-1)0.6000
=36.6°
find the value of θ, correct to one decimal place
43.6°
a pole is supported by a wire that runs from the top of the pole to a point on the level ground 6m from the base of the pole. the wire makes an angle of 47° with the ground.
find the height of the pole, correct to two decimal places
height of the pole = 6.43m
a 3m log rests with one end on top of a post and the other on the level ground 2.8m from the base of the post.
find the angle the log makes with the ground, correct to one decimal place
21.0°
a ladder rests on a wall 2m high. the foot of the ladder is 3m from the base of the wall on level ground.
find the angle the ladder makes with the ground, correct to one decimal place
33.7°
an airplane maintains a flight path of 17° with the horizontal after it takes off. it travels for 2km along this path.
find:
i) the horizontal distance of the airplane from its take-off point, and
ii) the height of the airplane above ground level
i) 1.91km
ii) 0.58km
the entrance to a horizontal mining tunnel has collapsed, trapping miners inside. the rescue team decide to drill a vertical escape shaft from a position 200m further up the hill. if the hill slopes at 23° from the horizontal, how deep does the rescue shaft need to be to meet the horizontal tunnel?
answer correct to one decimal place
78.1m
a strong rope needs to be fixed with one end attached to the top of a 5m pole and the other end pegged at an angle of 60° with the level ground.
Find the required length of the rope, correct to two decimal places
5.77m
from 300m away from the base of a tall building, on level ground, Elise measured the angle of elevation from the ground to the top of the building to be 54°.
Find the height of the building, to the nearest metre.
413m
The pilot of an airplane saw an airport at sea level at an angle of depression of 15°. Her altimeter showed that the airplane was at a height of 3,000m.
Find the horizontal distance of the airplane from the airport, to the nearest meter.
11,196m
When Darcy looked from the top of a cliff, 60m high, he noticed Elizabeth at an angle of depression of 20° on the ground below.
How far was Elizabeth from the cliff, correct to one decimal place
164.8m
a) find the length x, correct to one decimal place.
b) find the angle a, to the nearest degree
a) 44.6m
b) 36°
a) find the length x, correct to one decimal place
b) find the angle θ to the nearest degree.
a) 16.2m
b) 62°
a police helicopter hovering in a fixed position at an altitude of 500m moved its spotlight through an angle of depression of 57° onto a lost child. the pilot sighted the rescue team at an angle of depression of 31°. if the terrain was level, how far, to the nearest meter, was the rescue team from the child?
507m
state the three-figure bearing of each of the points A, B, C, and D
025°
state the three-point bearing of each of the points A, B, C and D
110°
state the three-figure bearing of each of the points A, B, C, and D
280°
eddie camped overnight at point A beside a river that ran eas-west. he walked on a bearing of 065° for 18km to point B.
a) what angle did his direction make with the river?
b) what is the shortest distance from B to the river, correct to two decimal places?
a) 25°
b) 7.61km
an airplane flew 500km south, then 600km east. give its three-figure bearing from its starting point, to the nearest degree
130°
a woman walked from point A for 10km on a bearing of 060° to reach point B. Then she walked for 15km heading south until she was at point D. Give the following distances correct to one decimal place and directions to the nearest degree.
a) find the distances walked from A to B and from B to D
b) how far south did she walk from B to C
c) find the distance from A to C
d) what is the distance from C to D
e) find the three-figure bearing and distance she would need to walk to return to her starting point
a) 10km, 15km
b) 5km
c) 8.7km
d) 10km
e) 319°, 13.2km
a ship left port P and sailed 20km on a bearing of 230°. it then sailed north for 30km to reach point C. Give the following distances correct to one decimal place and directions to the nearest degree.
a) find the distance AB
b) find the distance BP
c) find the distance BC
d) find the angle θ at point C
e) state the three-figure bearing and distance of the port P from the ship at C
a) 12.9km
b) 15.3km
c) 17.1km
d) 42°
e) 138°, 23.0km
find the area of the triangle
102cm²
find the area of the triangle
40cm²
find the area of triangle
25.7cm²
find the area of the triangle
26.0cm²
find the angle of the triangle
32.9cm²
find the angle of the triangle
10.8cm²
use heron’s rule to find the area of the triangle
36.0km²
use heron’s rule to find the area of the triangle
25.5cm²
use heron’s rule to find the area of the triangle
23.5cm²
find the area of the triangle
10cm²
find the area of the triangle
23.8cm²
find the area of the triangle
30.1m²
find the area of the triangle
100.9km²
find the area of a triable with a base of 28cm and a height of 16cm
224cm²
find the area of triable ABC with side a = 42cm, side b = 57cm, and angle of C = 70°
the kite shown is made using two sticks, AC and DB. the length of AC is 100cm and the length of DB is 70cm. find the area of the kite.
three students stretched a rope loop 12m long into different triangles. find the area of the triangle, where side A = 3m, B = 5m, and C = 4m.
6m²
a regular hexagon with sides 10cm long can be divided into six equilateral triangles.
a) find the area of each triangle
b) what is the area of the hexagon
a) 43.30cm²
b) 259.81cm²
a large rectangular area of land, ABCD in the diagram, has been subdivided into three regions as shown.
a) find the area of
i) region PAQ
ii) region QBCR
iii) region PQRD
b) find the size of the angle PQR, correct to one decimal
a)
i) 12km²
ii) 39km²
iii) 21km²
b) 29.6°
find the value of the unknown angle. use a + b + c = 180°
c = 50°
find the value of the unknown angle. use a + b + c = 180°
A = 40°
see 6H Q3 for sin rule questions
see 6H Q3 for sin rule questions
find angle B
41.0°
find angle C
53.7°
use the sine rule to find side B
19.60
using the sine rule, find side B
30.71
using the sine rule, find side A
55.38
find side B
67.94
find side B
67.84
solve (find all the unknown sides and angles of) the triangle
c = 10.16, b = 50.2°, c = 21.8°
solve (find all unknown sides and angles) of the triangle
b = 7.63, b = 20.3°, c = 39.7°
in the triable ABC, A = 105°, B = 39°, and a = 60. find side b
30.09
in the triangle ABC, B = 59°, C = 74°, c = 41. find sides a and b and angle A
a = 31.19, b = 36.56, A = 47
a fire-spotter located in a tower at A saw a fire in the direction 010°. 5km to the east of A, another fire-spotter at B saw the fire in the direction 300°.
find the distance of the fire from each other
2.66km from A, 5.2km from B
a surveyor standing at point A measured the angle of elevation to the top of the mountain as 30°. she moved 150m closer to the mountain and at point B measured the angle of elevation to the top of the mountain as 45°.
there is a proposal to have a strong cable from point A to the top of the mountain to carry tourists in a cable car. what is the length of the required cable?
409.81m
a naval officer sighted the smoke of a volcanic island on a bearing of 044°. a navigator on another ship 25km due east of the first ship saw the smoke on a bearing of 342°.
find the distance of each ship from the volcano
20.37km from naval ship, 26.93km from the other ship
using the cosine rule, find the unknown side
36.72
using the cosine rule, find the unknown side
47.62
using the cosine rule in the triangle ABC, a = 27, b = 22, C = 40°. find side c
find the lengths correct to two decimal places
17.41
using the cosine rule in triangle ABC, b = 42, c = 38, and A = 80°. find side a to two decimal places
51.51
use the cosine rule to find angle A to one decimal place
33.6°
using the cosine rule, find angle A to one decimal place
88.0°
in the triangle ABC, a = 31, b = 47, and c = 52. use the cosine rule to find angle B to one decimal place
63.2°
in the triangle ABC, a = 66, b = 29, and c = 48. find angle C using the cosine rule to one decimal place
40.9°
using the cosine rule, find angle A in the triangle
88.0°
using the cosine rule, find angle A in the triangle
110.7°
in the triangle ABC, a = 9, b = 10, and c = 11. find angle A. calculate angle to one decimal place
50.5°
in the triangle ABC, a = 16, b = 21, and c = 19. find the largest angle. calculate lengths correct to two decimal places and angles correct to one decimal place
B = 73.2°
a farm has a triangular shape with fences of 5km, 7km, and 9km in length. find the size of the smallest angle between the fences. (the smallest angle is always opposite the smallest side)
33.6°
a ship left the port P and sailed 18km on a bearing of 030° to point A. another ship left port P and sailed 20km east to point B. find the distance from A to B, correct to one decimal place
19.1km
a bushwalker walked 12km west from point A to B. her friend walked 14km from point A to point C, as shown in the diagram. the distance from B to C is 9km.
a) find the angle A, between the paths taken by the bushwalkers, correct to one decimal place
b) what is the bearing of point C from A? give the bearing correct to the nearest degree
a) 39.6°
b) 310°
Note
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