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Solving Right Angled Triangles Using Trigonometry
1 Find the value of each of the following.
(a) cos 15°
(b) sin 21°
(c) tan 44°
(d) csc 72°
(e) cot 64°
(f) sec 24°
(g) tan 51°
(h) sec 87°
(i) cot 47°
6 Refer to the diagram. (a)
Which trigonometric ratio
can you use to write an
equation to solve for  A?
(b) Write an equation to
solve for  A. Solve the
equation.
7 In each triangle find the measure of angle θ
2 Find the measure of each angle A.
(a) sin A = 0.9703
(b) cos A = 0.8090
(c) tan A = 0.8693
(d) tan A = 4.0108
3 A (e)
diagram
cos A is
= shown.
0.4540
(f) sin A = 0.3511
(a) Which
trigonometric ratio
can you use to
write an equation
to solve for x?
(b) Write an equation to
solve
for x.
Solve
4 Refer
to the
diagram.
the
equation.
(a) Which
trigonometric ratio can
you use to write an
equation to solve for
k?
(b) Write an equation to
solve for k. Solve
8 Solve the following triangles. Draw a diagram to
help you record the given information.
(a) In XYZ,  X = 90°,  Y = 15°, x = 73.6
(b) In DEF,  D = 90°,  F = 37°, f = 3.12
(c) In ABC,  B = 90°, b = 40.3, a = 29.0
(d) In  POR,  R = 90°, r = 48.7, q = 46.5
(e) In LMN,  L = 90°, m = 76.1, n = 37.5
(f) In GHI,  H = 90°, g = 45.4, 1 = 153.2
(g) In RST,  T = 90°, r = 62.1, s = 78.4
(h) In XYZ,  X = 90°, y = 24.9, z = 40.8
the equation.
5 In each triangle find the missing measure
shown by a variable.
9 The ramp up to a delivery
truck is 2.10 m long. If
the ramp makes an
angle of 25° with the
ground, what is the
height to the truck?
10 A ladder 5.0 m long
reaches a wall at a
point 4.6 m from the
ground. What angle
does the ladder make
with the ground?
11 The arm of a crane makes an angle of 35° with the horizontal. How , high above the
ground is the end of the crane arm?
12 A tow truck raises the front end of a car 0.85 m above the ground. If the car is
3.72 m long, what angle does the car make with the ground?
13 A ski slope falls a vertical height of 550 m for a distance of 1750 m travelled
down the ski run. What is the angle of the ski slope?
14 A conveyor belt is 12.8 m long. The belt is inclined at an angle of 12°. What length
of space is needed horizontally for this conveyor belt?
15 When a tent rope is 1.8 m long it makes an angle of 42° with the
ground. If the rope is shortened 0.3 m, what angle will it make with
the ground?
1a)0.9659 b)0.3584 c)0.9657 d)1.0515 e)0.4877 ()1.0946 g)1.2349 h)19.1073
i)0.9325 2a)76° b)36° c)41° d)76° e)63° f)21°
3a)sin x
b)sin 42° = 402'
x = 269
4a)tan K b)tan 32° = 1 6 , k = 10 5a)5.9 b)3.3 c)175 d)20.3
6a)sln A 12 b)sin A = 1 , LA =49'
7a)54°
b)63° 6
8a)  Z = 75°, y = 19.0, z = 71.1 b) E=53°, d=5.2, e=4.1
c)  A = 46°,  C = 44°, c = 28.0 d) P=17°,  Q=73°,p=14.2 e) M =64°,  N
=26°, /=84.8 f)  G = 17°, L I = 73°, h = 159.8 g)  R = 38°,  S = 52°,
t = 100.0 h) Y=31°,  Z=59°,x=47.8
9)0.9 m 10)67° 11)98.7 m 12)13° 13)18° 14)12.5 m 15)53°