SOLVING FOR MISSING SIDE IN RIGHT TRIANGLE WITH TRIGONOMETRY

To find missing sides of right triangle, we have to mark which is is hypotenuse, opposite and adjacent.  

Based on the side what we know and the side what we find, including these two information we have to decide which trigonometric ratio should be used.

Set up a trigonometric equation connecting the angle with the sides given :

Problem 1 :

Solution :

a = hypotenuse

x = opposite side

sin θ = opposite side/hypotenuse

sin 68° = x/a

0.927 = x/a

x = 0.927a

Problem 2 :

Solution :

b = hypotenuse

x = adjacent side

cos θ = adjacent side/hypotenuse

cos 37° = x/b

0.798 = x/b

x = 0.798b

Problem 3 :

Solution :

c = adjacent side

x = opposite side

tan θ = opposite/adjacent

tan 58° = x/c

1.6 = x/c

x = 1.6c

Problem 4 :

Solution :

d = adjacent side

x = hypotenuse

cos θ = adjacent/hypotenuse

cos 42° = d/x

0.74 = d/x

x = d/0.74

Problem 5 :

Solution :

e = opposite side

x = adjacent side

tan θ = opposite side/adjacent

tan 51° = e/x

1.23 = e/x

x = e/1.23

Problem 6 :

Solution :

f = opposite side

x = adjacent side

tan θ = opposite side/adjacent

tan 71° = f/x

2.90 = f/x

x = f/2.90

Find, to 2 decimal places, the unknown length in:

Problem 7 :

Solution :

Opposite side = x cm

Hypotenuse = 9 cm

sin θ = opposite/hypotenuse

sin 68° = x/9

0.92 = x/9

x = 0.92 × 9

x = 8.28 cm

Problem 8 :

Solution :

Here, adjacent side = x cm

Hypotenuse = 10 cm

cos θ = adjacent/hypotenuse

cos 37° = x/10

0.79 = x/10

x = 0.79 × 10

x = 7.99 cm

Problem 9 :

Solution :

Here, Opposite side = x cm

Adjacent side = 3.82 cm

tan θ = opposite/adjacent

tan 58° = x/3.82

1.60 = x/3.82

x = 1.60 × 3.82

x = 6.11 cm