Page 36 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 2] VECTORS 21

SOLVED PROBLEM 2.5
Find the values of the sine, cosine, and tangent of angle θ in Fig. 2-9.

opposite side 3cm
sin θ = = = 0.6
hypotenuse 5cm
adjacent side 4cm
cos θ = = = 0.8
hypotenuse 5cm
opposite side 3cm
tan θ = = = 0.75
adjacent side 4cm

Fig. 2-9

SOLVED PROBLEM 2.6
In the triangle of Fig. 2-8, c = 80 cm and θ = 30 . Find the values of a, b, and φ.
◦
We start with the length of the side a:
a
sin θ =
c
◦
a = c sin θ = (80 cm)(sin 30 ) = 40 cm
To find b, we can proceed in two ways. In the first way we note that
b
cos θ =
c
◦
b = c cos θ = (80 cm)(cos 30 ) = 69 cm
The other way is to use the Pythagorean theorem:

2
2
2
2
b = c − a = (80 cm) − (40 cm) = 69 cm
SOLVED PROBLEM 2.7
In the triangle of Fig. 2-8, a = 70 m and b = 100 m. Find the values of c, θ, and φ.
To find c, we use the Pythagorean theorem:

2 2 2 2
c = a + b = (70 m) + (100 m) = 122 m
To find θ, we proceed in the following way:
a 70 m
tan θ = = = 0.70
b 100 m
θ = tan −1 0.70 = 35 ◦
Since θ = 35 ,
◦
◦
φ = 90 − θ = 90 − 35 = 55 ◦
◦
◦